>i 


4 


V 


PRACTICAL  INSTRUCTIONS 


RELATING  TO  THE  CONSTRUCTION  AND  USE  OF  THE 


STEAM  ENGINE  INDICATOR 


PAET  I 

SENERAL  DESIGN  AND  CONSTRUCTION  OF  STEAM  ENGINE 
INDICATORS 

SPECIAL  DESIGN,  CONSTRUCTION  AND  USE 
OF  THE 

CROSBY  INDICATOR 


PAET  II 
APPLICATIONS  OF  THE  INDICATOR 

PART  III 

PROPERTIES  OF  STEAM  AND  OF    PERFECT  GASES 

DESIGN  OF  A  PLAIN  SLIDE  VALVE 

VALVE  SETTING  ON  PLAIN  SLIDE  VALVE  ENGINES  AND 
ON  CORLISS  ENGINES 


PARTS  II  AND  III 
By  EDWARD  F.  MILLER 

Pro/e.i.sor  nf  Stcnm  Eiifiiiitfrinri 
Massachusetts  Institute  of  Technology 


PUBLISHED  BY  THE 

CROSBY  STEAM  GAGE  AND  VALVE  COMPANY 

Boston,  Massachusetts,  U.S.A. 
1911 


Copyright,  1911,  by 
Crosby  Steam  Gage  and  Valve  Company 


QKO.    H.    ELLIS    CO. 
PRINTERS,    BOSTON 


INTRODUCTION 


The  purpose  of  this  book  is  to  enable  any  engineer,  First, 
To  understand  the  design,  construction  and  use  of  the 
Crosby  Steam  Engine  Indicator.  Second,  To  make  suitable 
preparation  for  applying  it  to  a  steam  engine,  and  attach- 
ing the  mechanism  for  operating  the  paper  drum.  Third, 
To  take  diagrams,  read  them  intelligently,  and,  after  some 
experience,  to  deduce  from  them  such  information  concern- 
ing the  working  of  an  engine  as  a  good  instrument  skilfully 
applied  and  handled  is  capable  of  revealing  to  the  studious 
and  observing  mind. 

Crosby  Steam  Gage  and  Valve  Company 

Boston,  Sept.  1,  1911 


CONTENTS 


PART  I 


CHAPTER    I 


The  Steam  Engine  Indicator 1 

Diagram  Lines  Explained 6 

Definitions  of  Technical  Terms 9 


CILYPTER   II 

The  Crosby  Steam  Engine  Indicator 16 

The  Crosby  Standard  Steam  Engine  Indicator     ...  18 

The  Crosby  New  Steam  Engine  Indicator 24 

The  Crosby  New  Indicator  No.  2 27 

The  Crosby  Indicator  with  Drum  for  Taking  Continu- 
ous Diagrams 29 

The  Lanza  Continuous  Diagram  Appliance     ....  32 

CHAPTER   III 

The  Crosby  Gas  Engine  Indicator 33 

The  Crosby  Combined  Gas  and  Steam  Engine   Indi- 
cator    34 

The  Crosby  Anmaonia  Indicator 34 

The  Crosby  Ordnance  Indicator 35 

The  Crosby  Hydraulic  Indicator 36 

'  CHAPTER    IV 

Indicator    Attachments     and     Accessory     Apparatus 

Needed  in  Making  Tests 37 

Sargent  Improved  Electrical  Attachment 37 

Cro.sby  Standard  Indicator  with  Detent 42 

Planimeters 43 

Tlu-ottling  Calorimeter 49 

V 


COXTEXTS 
CHAPTER  V 

How  to  Handle  and  Take  Care  of  a  Crosby  Indicator  55 

Indicator  Springs 59 

Indicator  Scales 60 

CHAPTER  VI 

How  and  Where  to  Attach  the  Indicator       62 

CHAPTER  VII 

Drum  Motion 65 

Reducing  Lever 65 

Brumho  Pulley 67 

Pantograph 69 

Crosby  Reducing  Wheel 71 

Crosby  Reducing  Wheel  with  Detent 73 

Crosby  Reducing  Wheel  with  Recording  Counter   .      .  74 

Testing  the  Accuracy  of  Reducing  Mechanism  ...  77 

CHAPTER  VIII 

How  to  Take  Diagrams 78 

CHAPTER  IX 

How  to  Find  the  Power  of  an  Engine 81 

The  Piston  Area 81 

The  Travel  of  the  Piston 81 

The  Mean  Effective  Pressure 81 

Calculating  I.  H.  P 86 

Discussion  of  M.  E.  P 86 

Calculating  H.  P.  of  Gas  Engine,  Otto  Fouy-Cycle     .  88 

Calculating  H.  P.  of  Gas  Engine,  Two-Cycle      ...  93 

Theoretical  Efficiency  of  a  Four-Cycle  Gas  Engine      .  93 

Actual  Efficiency  of  a  Gas  Engine 93 

CHAPTER  X 

The  Hyperljolic,  Curve 94 


CONTENTS 

PART  II 

Applications 103 

PART  III 

CHAPTER  I 

Properties  of  Steam  and  of  Perfect  Gases     .      .      .      .  123 

Properties  of  Saturated  Steam 124 

Properties  of  Superheated  Steam 128 

Heat    Consumption    and    Thermal    Efficiency    of    aii 

Engine 132 

Carnot  Engine 133 

Non-Conducting  Engine 135 

Temperature  Entropy  Chart       . 137 

Flow  of  vSteam  through  an  Orifice 140 

Measurement  of  Dry  Steam  by  the  Flow  through  an 

Orifice 141 

Design  of  a  Tiirbine  Nozzle  for  Complete  Expansion  141 

Calculating  the  Size  of  a  Steam  Main 144 

Characteristic  Equation  for  Perfect  Gases  and  its  Ap- 
plication      146 

Measurement  of  Air  by  the  Flow  through  an  Orifice  .  148 

Isothermal  Lines     .     .     , 148 

Compressing  Air 150 

Calculation  of  Power  Needed  for  a  Compressor       .      .  150 

Stage  Compression 151 

Probable  Horse])ower  of  an  Engine 153 

CHAPTER  II 

Method  of  Calculating  from  the  Indicator  Card  from 
a  Steam  Engine,  the  Per  Cent  of  Mixture  Accounted 

for  as  Steam  at  CutH)f¥  and  at  Release      .      .      .      .  155 


CONTENTS 


CHAPTER   III 


Design  of  a  Plain  Slide  Valve 158 

Valve  Setting  on  a  Plain  Slide  Valve  Engine  and  on 

a  Corliss  Engine 158 

Explanation  and  Use  of  Zeuner  Diagram 160 

Laying  Out  a  Plain  Slide  Valve 165 

Setting  a  Plain  Slide  Valve  Gear 166 

Setting  a  Corliss  Valve  Gear 166 

Explanation  and  Use  of  Logarithms 168 


TABLES 

Logarithms 172 

Areas  and  Circumferences  of  Circles 174 

Weight  of  a  Cubic  Foot  of  Water 182 

Charts  Giving  the  Values  of  the  Temperature,  Heat 
of  the  Liquid,  Total  Heat,  Latent  Heat,  and  Specific 
Volume,  Between  0  and  10  Pounds   Absolute  and 
Between  10  Pounds  and  250  Pounds  Absolute  .     .     182a-& 
Temperature  Entropy  Chart 182c 


APPENDIX 

Crosby  Revolution  Counter 185 

Crosby  Square  Counter 187 

Crosby  Locomotive  Counter 187 

Crosby  Recording  Counter 188 

Crosby  Pressure  and  Vacuum  Gages 190 

Crosby  Pressure  Recorder 191 

Crosby  Pressure  Recorder  and  Gage 193 

Thermometers 195 

Lanza  Continuous  Diagram  Appliance 196 

Crosby  Lidicator  Awards .,.,..  201 


PRACTICAL  INSTRUCTIONS 

KELATINO    TO    THE    CONSTRUCTION 
AND    USE    OF    THE 

STEAM  ENGINE  INDICATOR 


PAET  I 


CHAPTER  I 


THE  STEAM  ENGINE  INDICATOR 

The  steam  engine  indicator,  invented  by  James  Watt,  and 
long  kept  secret,  was  for  many  years  after  its  secret  became 
known,  strangely  neglected  by  most  makers  and  users  of 
steam  engines. 

The  earlier  forms  of  the  instrmnent,  which  preceded  that 
invented  by  Richards,  were  so  imperfect  and  so  ill-adapted 
to  engines  running  at  other  than  very  low  speeds,  that  their 
indications  were  often  misleading,  more  often  unintelligible, 
and  seldom  of  much  value  beyond  revealing  the  point  of 
stroke  at  which  the  valves  ojjened  and  closed :  a  most  valu- 
able service,  alone  worth  the  cost  of  an  indicator,  but  only 
a  small  part  of  the  service  to  be  obtained  from  a  really  good 
instrument. 

The  general  princijiles  on  which  the  best  type  of  the 
steam  engine  indicator  is  designed,  may  be  briefly  stated  as 
follows : 

A  piston  of  carefully  determined  area  is  nicely  fitted  into 
a  cylinder  so  that  it  will  move  up  and  down  without  sensible 

1 


Z  THE  STEAM  ENGIXE  INDICATOR 

friction.  The  cylinder  is  open  at  the  bottom  and  fittea  so 
that  it  may  be  attached  to  the  cylinder  of  a  steam  engine 
and  have  free  communication  with  its  interior,  by  which 
arrangement  the  under  side  of  the  piston  is  subjected  to  the 
varying  pressure  of  the  steam  acting  therein.  The  upward 
movement  of  the  piston  —  due  to  the  pressure  of  the  steam  — 
is  resisted  by  a  spiral  spring  of  known  resilience.  A  piston 
rod  projects  upward  through  the  cylinder  cap  and  moves  a 
lever  having  at  its  free  end  a  pencil  point,  whose  vertical 
movement  bears  a  constant  ratio  to  that  of  the  piston.  A 
drum  of  cylindrical  form  and  covered  with  paper  is  attached 
to  the  cylinder  in  such  a  manner  that  the  j^encil  point  may 
be  brought  in  contact  with  its  surface,  and  thus  record  any 
movement  of  either  paper  or  pencil ;  the  drum  is  given  a 
horizontal  motion  coincident  Avith  and  bearing  a  constant 
ratio  to  the  movement  of  the  piston  of  the  engine.  It  is 
moved  in  one  direction  by  means  of  a  cord  attached  to  the 
crosshead  and  in  the  opposite  direction  by  a  spi'ing  within 
itself. 

When  this  mechanism  is  properly  adjusted  and  free  com- 
munication is  opened  with  the  cylinder  of  a  steam  engine  in 
motion,  it  is  evident  that  the  pencil  will  be  moved  vertically 
by  the  varying  pressure  of  steam  under  the  piston,  and  as 
the  drum  is  rotated  by  the  reciprocating  motion  of  the  en- 
gine, if  the  pencil  is  held  in  contact  v\dth  the  moving  paper 
during  one  revokition  of  the  engine,  a  figure  or  diagram  will 
be  traced  representing  the  pressure  of  steam  in  the  cylinder ; 
the  upper  line  showing  the  pressure  urging  the  engine 
piston  forward,  and  the  lower  the  pressure  retarding  its 
movement  on  the  return  stroke. 

To  enable  the  engineer  to  more  correctly  interpret  the 
nature  of  the  pressures,  the  line  showing  the  atmospheric 
pressure  is  drawn  in  its  relative  position,  which  indicates 
whether  the  jiressvire  at  any  part  is  greater  or  less  than  that 
of  the  atmosphere. 


WHAT  IS  THE  OUOD  OF  AX  INDICATOR  ?  8 

From  such  a  diagram  may  be  deduced  many  particulars 
which  are  of  supreme  miportance  to  engine  builders,  engi- 
neers, and  the  owners  of  steam  plants. 

WHAT  IS  THE  GOOD  OF  AN  INDICATOR? 

This  question  was  asked  by  a  young  engineer  who  had 
come  to  examine  and  purchase  a  Crosby  indicator,  with  a 
view  to  rendering  his  services  of  greater  value  to  his  em- 
ployer, by  a  knowledge  and  use  of  that  instrument.  His 
question  was  overheard  by  the  proprietor  of  a  large  estab- 
lishment in  the  city  of  Worcester,  Mass.,  who  took  occ'asion 
to  re])ly  as  follows  : 

"  I  will  tell  you  what  good  an  indicator  did  at  our  works. 
Our  steam  engine  was  not  giving  sufficient  power  for  our 
business,  and  we  expected  to  be  obliged  to  procure  a  larger 
one.  A  neighbor  suggested  that  we  have  our  engine  indi- 
cated to  see  if  we  were  getting  the  best  service  obtainable 
from  it.  This  was  done  with  a  Crosby  indicator,  and  the 
result  was  that  when  the  valves  were  properly  adjusted  and 
other  slight  changes  made  we  had  ample  power,  and  the 
improved  condition  of  the  engine  made  a  reduction  in  our 
coal  bills  during  the  following  year  of  $500." 

Another  case  :  An  expert  engineer  was  called  to  indicate 
several  locomotives  just  completed  by  one  of  our  prominent  lo- 
comotive builders,  who  had  in  use  a  large  Corliss  engine,  which ' 
had  been  running  only  a  few  months.  When  the  locomotives 
were  indicated,  the  pi-oprietor  proposed  that  the  indicator  be 
applied  to  the  Corliss  engnie,  the  engineer  of  which  remarked, 
"  Guess  you'll  find  her  all  right,  as  she's  running  fine." 

The  first  card  showed  that  nearlij  all  the  ivork  was  being 
done  at  one  end  of  the  cyUnder.  The  valves  were  changed 
and  a  great  improvement  was  apparent  in  the  running  of 
the  engine,  while  the  actual  consunq)tion  of  coal  was  reduced 
from  an  average  of  3,370  pounds  per  day,  before  the  change 
was  made,  to  2.338  pounds  afterwards. 


4  INDICATOR  DIAGRAMS 

These  two  instances  are  valuable  in  showing  "  the  good  of 
an  indicator." 

Items  of  Information  to  be  obtained  by  the  use  of  the 
Indicator 

The  arrangement  of  the  valves  for  admission,  cut-off, 
release  and  compression  of  steam. 

The  adequacy  of  the  ports  and  passages  for  admission 
and  exhaust,  and  when  applied  to  the  steam  chest,  the 
adequacy  of  the  steam  pipes. 

The  suitableness  of  the  valve  motion  in  point  of  rapidity 
at  the  right  time. 

The  quantity  of  power  developed  in  the  cylinder,  and  the 
qiiantity  lost  in  various  ways :  by  wire  drawing,  by  back 
l)ressure,  by  premature  release,  by  mal-adjustment  of  valves, 
l)y  leakage,  etc. 

It  is  useful  to  the  designers  of  steam  engines,  as  by  prop- 
erly combining  the  cards  the  effective  pressure  on  the  piston 
at  any  point  can  be  determined,  and  from  this  the  rotative 
effect  or  the  rotating  force  acting  at  right  angles  to  the 
crank  can  be  calculated. 

Taken  in  combination  with  measurements  of  feed  water 
and  the  condensation  and  measurement  of  the  exhaust  steam, 
with  the  amount  of  fuel  used,  the  indicator  furnishes  many 
other  items  of  importance  when  the  economical  generation 
and  use  of  steam  are  considered. 

For  every  one  of  these  purposes  it  is  important  that  the 
diagrams  traced  by  the  indicator  should  truly  represent  the 
path  of  the  piston  and  the  pressure  exerted  on  both  sides  of 
the  piston  at  every  point  of  that  path. 

INDICATOR  DIAGRAMS 

The  degree  of  excellence  to  which  steam  engines  of  the 
present  time  have  been  brought  is  due  more  to  the  use  of 
the  indicator  than  to  any  other  cause,  as  a  careful  study  of 
indicator  diagrams  taken  under  different  conditions  of  load, 


ANALYSIS  OF  THE  DIAGRAM  5 

pressure,  etc.,  is  the  only  means  of  becoming  familiar  with 
the  action  of  steam  in  an  engine,  and  of  gaining  a  definite 
knowledge  of  the  various  changes  of  pressure  that  take 
place  in  the  cylinder. 

An  indicator  diagram  is  the  result  of  two  movements, 
namely :  a  horizontal  movement  of  the  paper  in  exact  corre- 
spondence with  the  movement  of  the  piston,  and  a  vertical 
movement  of  the  pencil  in  exact  ratio  to  the  pressure  exerted 
in  the  cylinder  of  the  engine  ;  consequently,  it  represents  hy 
its  length  the  stroke  of  the  engine  on  a  reduced  scale,  and 
hy  its  height  at  any  point,  the  pressure  on  the  piston  at  the 
corresponding  point  in  the  stroke.  The  shape  of  the  diagram 
depends  altogether  upon  the  manner  in  which  the  steam  is 
admitted  to  and  released  from  the  cylinder  of  the  engine ; 
the  variety  of  shapes  given  from  different  engines,  and  by 
the  same  engine  under  different  circumstances,  is  almost 
endless,  and  it  is  in  the  intelligent  and  careful  measurement 
of  these  that  the  true  value  of  the  indicator  is  found,  and  no 
one  at  the  present  day  can  claim  to  be  a  competent  engineer 
who  has  not  become  familiar  with  the  use  of  the  indicator, 
and  skilful  in  tui-ning  to  practical  advantage  the  varied 
information  which  it  furnishes. 

A  diagram  shows  the  pressure  acting  on  one  side  of  the 
piston  only,  during  both  the  forward  and  return  stroke, 
whereon  all  the  changes  of  pressure  may  be  properly  located, 
studied,  and  measured.  To  show  the  corresponding  pres- 
sures on  the  other  side  of  the  piston,  another  diagram  must 
be  taken  from  the  other  end  of  the  cylinder.  When  the 
tlii"ee-way  cock  is  used,  the  diagrams  from  both  ends  are 
usually  taken  on  the  same  paper,  as  in  Fig.  2. 

ANALYSIS  OF  THE  DIAGRAM 

The  names  by  which  the  various  points  and  lines  of  an 
indicator  diagram  are  known  and  designated  are  given  on 
the  page  following.      See  Fig.  1. 


DIAGRAM  LINES  EXPT.AIXER 


The  closed  figure  or  dia- 
gram, C  D  E  F  G  H  is 
drawn  by  the  indicator, 
and  is  the  result  of  one  in- 
dication from  one  side  of 
the  piston  of  an  engine. 
The  straight  line   A  B  is 


Fig.  1 

also  drawn  by  the  indicator,  but  at  a  time  when  steam  con- 
nection Avith  the  engine  is  closed,  and  both  sides  of  the  indi- 
cator piston  are  subjected  to  atmospheric  pressure  only. 

The  straight  lines  O  X,  O  Y,  and  J  K,  when  required, 
are  drawn  by  hand  as  explained  below,  and  may  be  called 
reference  lines. 

DIAGRAM  LINES  EXPLAINED 

The  admission  line  C  D  shows  the  rise  in  pressure  due 
to  the  admission  of  steam  to  the  cylinder  by  the  opening  of 
the  steam  valve.  If  the  steam  is  admitted  quickly  when 
the  engine  is  about  on  the  dead-center  this  line  will  be 
nearly  vertical. 

The  steam  line  D  E  is  drawn  when  the  steam  valve  is 
open  and  steam  is  being  admitted  to  the  cylinder. 

The  point  of  cut-off  E  is  the  point  where  the  admission  of 
steam  is  stopped  by  the  closing  of  the  valve.  It  is  some- 
times difficult  to  determine  the  exact  point  at  which  the 
cut-off  takes  place.  It  is  usually  located  Avhere  the  outline  of 
the  diagram  changes  its  curvature  from  convex  to  concave. 


REFERENCE  LIXES  EXPLAINED  i 

The  expansion  curve  E  F  shows  the  fall  in  pressure  as 
the  steam  in  the  cylinder  expands  behind  the  moving  piston 
of  the  engine. 

The  point  of  release  Y  shows  when  the  exhaust  valve 
opens. 

The  exhaust  line  F  G  represents  the  loss  in  pressure 
which  takes  place  when  the  exhaust  valve  opens  at  or  near 
the  end  of  the  stroke. 

The  hack  2»'e-'isitre  line  G  H  shows  the  pressure  against 
which  the  piston  acts  during  its  return  stroke.  On  diagranis 
taken  from  non-condensing  engines  it  is  either  coincident 
with  or  above  the  atmospheric  line,  as  in  Fig.  1.  On  cards 
taken  from  a  condensing  engine,  however,  it  is  found  below 
the  atmospheric  line,  and  at  a  distance  greater  or  less, 
according  to  the  vacuum  obtained  iii  the  cylinder.   . 

The  j^oint  of  exhaust  closure  His  the  point  where  the 
exhaust  valve  closes.  It  cannot  be  located  veiy  definitely, 
as  tlie  change  in  pressure  is  at  first  due  to  the  gradual 
closing  of  the  valve. 

The  compression  curve  H  C  shows  the  rise  in  pressure 
due  to  the  compression  of  the  steam  remaining  in  the  cylin- 
der after  the  exliaust  valve  has  closed. 

The  atmospheric  line  A  B  is  a  line  drawn  by  the  pencil 
of  the  indicator  when  its  connections  with  the  engine  are 
closed  and  both  sides  of  the  piston  are  open  to  the  atmos- 
phere. This  line  represents  on  the  diagram  the  pressure  of 
the  atmosphere,  or  zero  of  the  steam  gage. 

REFERENCE  LINES  EXPLAINED 

The  zero  line  of  pressure,  or  line  of  absolute  vacuum,  O  X, 
is  a  reference  line,  and  is  drawn  by  hand,  14  ^^  pounds  by 
the  scale,  below  and  parallel  with  the  atmospheric  line.  It 
represents  a  perfect  vacuum,  or  absence  of  all  ])ressure. 

The  line  of  boiler  pressure  i  K  is  drawn  by  hand  parallel 
to  the  atmospheric  line  and  at  a  distance  from  it  by  the  scale 


O  DERANGED  VALVE  MOTION 

equal  to  the  boiler  pressure  shown  hy  the  steam  gage.     The  ; 
difference  in  pounds  between  it  and  the  line  of  the  diagram  i 
D  E  shows  the  pressure  which  is  lost  after  the  steam  has  I 
flowed  thi'ough  the  contracted  passages  of  the  steam  pipes 
and  the  ports  of  the  engine. 

The  clearance  line  O  Y  is  another  reference  line  drawn 
at  right  angles  to  the  atmospheric  line  and  at  a  distance 
from  the  end  of  the  diagram  equal  to  the  same  per  cent  of 
its  length  as  the  cleai-ance  bears  to  the  piston  travel  or  dis- 
placement. The  distance  between  the  clearance  line  and 
the  end  of  the  diagram  represents  the  volume  of  the  clear- 
ance and  waste  room  of  the  ports  and  passages  at  that  end 
of  the  cylinder. 


DERANGED  VALVE  MOTION 


Fig.  2 

In  Fig.  U  the  lighter  lines  show  two  diagrams,  one  from 
each  end  of  the  cylinder  of  a  single  valve  liigh  pressure  en- 
gine. This  valve  admits  the  steam  over  its  ends  and  ex- 
hausts inside.  The  derangement  is  caused  by  the  valve 
stem  being  too  long  ;  consequently,  at  the  l)ack  end  the 
diagram  shows  that  the  steam  was  admitted  late,  cut  off 
early,  exhausted  early,  and  the  exhaust  valve  closed  late,  so 
that  there  is  little  or  no  compression.  The  diagram  at  the 
crank  end  shows  the  opposite  defects,  viz.,  steam  is  admitted 
too  soon  and  carried  too  far  on  the  stroke,  the  exhaust  valve 


UNITS  OF  MEASUREMEXT  \j 

is  opened  too  late  ami  closed  too  soon  to  get  the  steam  well 
out  of  the  cylinder,  causing  excessive  hack  pressure,  even 
greater  than  the  hoiler  pressure,  as  shown  hy  the  loop  at  the 
top. 

To  remedy  this  derangement,  the  valve  stem  should  be 
shoi'tened  hy  the  screw  threads  at  one  end.  It  may  then  he 
found  that  the  steam  valve  opens  a  little  too  late  at  hoth 
ends,  and  it  will  therefore  he  necessary  to  turn  the  eccentric 
ahead  on  the  shaft  until  hoth  diagrams  resemble  the  figure 
shown  l)y  the  hea^^est  Une. 

UNITS  OF  MEASUREMENT  AND  TECHNICAL  TERMS 

All  substances  of  whatever  nature  are  measurable,  and 
their  measurements  are  referable  to  some  established  units, 
to  be  properly  expressed  and  dealt  with.  An  intimate  knowl- 
edge of  some  of  these  is  indispensable  to  the  engineer  ;  a  few 
are  here  briefly  defined. 

The  unit  of  linear  measiirement  is  the  inch,  or  one- 
twelfth  part  of  a  foot. 

The  unit  of  superficial  Tneasurement  is  the  square  inch. 

The  unit  of  solid  measuretnent  is  the  cubic  inch. 

The  unit  of  fluid  ^9/*e.s.5«re  is  the  pound  avoirdupois, 
consisting  of  7,000  gi*ains. 

The  wilt  of  elasticiti/,  or  the  pressure  exerted  by  elastic 
fluids,  is,  for  popular  use,  1  pound  on  1  square  inch. 

The  unit  of  work  or  potver  is  1  pound  lifted  12  inches, 
or,  in  other  words,  1  pound  of  force  acting  through  1  foot  of 
distance,  and  is  caUed  the  foot-pound.  As  a  foot-pomid  is 
the  amount  of  work  done  in  raising  1  pound  through  the 
distance  of  1  foot,  an  equivalent  amount  of  work  would  be 
raising  ^  pound  2  feet,  or  12  pounds  1  inch. 

Horsepower.  The  standard  used  for  measuring  the 
power  of  a  steam  engine  is  the  horsepower.  It  was  origi- 
nally determined  by  James  Watt  from  experiments  made 
on  London  drayhorses.      It  is  considerably  above  the  power 


10  TECHNICAL  TERMS 

of  an  ordinary  horse,  and  is  now  simply  an  arbitrary  stand- 
ard. It  is  equal  to  33,000  foot-pounds  exerted  during  one 
minute  of  time,  or  550  foot-pounds  during  one  second. 

Indicated  horsepo^ver  is  the  horsepower  of  an  engine  as 
found  by  the  use  of  a  steam  engine  indicator,  and  is  thus 
expressed  :  I.  H.  P. 

Net  horsepoivei'  is  the  indicated  horsepower  of  an  en- 
gine, less  the  horsepower  which  is  consumed  in  overcom- 
ing its  own  friction. 

Wire  drawing,  as  applied  to  steam,  is  the  reducing  of  its 
presstire,  due  to  its  floA\ang  through  restricted  or  crooked 
pipes  and  passages. 

Absolute  pressure  is  pressure  reckoned  from  absolute 
vacumn ;  in  other  words,  it  is  the  pressure  of  any  fluid  as 
shown  by  a  pressure  gage,  with  the  weight  or  pressure  of  the 
atmosphere  added  thereto. 

Initial  forward  pressure  in  a  cyhnder  is  the  pressure 
acting  on  the  piston  at  or  near  the  beginning  of  the  foi-ward 
stroke. 

Terminal  forward  pressiire  is  the  pressure  above  the 
Une  of  perfect  vacuum  that  would  exist  at  the  end  of  the 
stroke  if  the  steam  had  not  been  released  earlier.  It  may 
be  found  by  continuing  the  expansion  curve  to  the  end  of 
the  diagram,  as  in  Fig.  1  at  F,  or  it  may  be  taken  at  the 
point  of  release.  This  pressure  is  always  measured  from 
the  line  of  perfect  vacuum,  hence  it  is  the  absolute  terminal 
pressure. 

Mean  effective  pressure  (written  as  M.  E.  P.)  is  that 
equivalent  constant  pressure  which  will  do  the  same  amount 
of  work  on  the  piston  per  stroke  as  is  done  by  the  varying 
pressure  shown  by  the  indicator  card.  This  may  be  calcu- 
lated by  dividing  the  area  of  the  card  by  the  length  and 
multiplying  by  the  scale  of  the  spring  used  in  the  indicator, 
or  it  may  be  obtained  by  taking  the  average  of  a  number  of 
pressures  measured  between  the  top  and  the  bottom  lines  of 


TECHNICAL  TERMS  11 

the  card  at  equidistant  intervals  along  the  length  of  the  card. 
This  is  illustrated  more  fully  on  page  85. 

Piston  displacemeyit  is  the  space  in  the  cyhnder  swept 
through  by  the  piston  in  its  travel.  It  is  reckoned  in  cubic 
feet,  and  is  found  by  multipljang  the  net  area  of  the  piston 
in  square  feet  by  the  length  of  stroke  in  feet,  allowance 
being  made  for  the  piston  rod. 

Clearance  is  all  the  waste  room  or  space  at  either  end  of 
the  cylinder,  between  its  head  and  the  piston  when  on  a 
dead  center,  including  the  counterbore  and  the  ports,  up  to  the 
face  of  the  closed  valves.  Clearance  is  generally  given  as  a 
percentage  of  the  piston  displacement.  Many  of  the  modern 
steam  engines  have  clearances  no  gi'eater  than  2\  per  cent. 

The  number  of  expansions  is  the  nimiber  of  times  the 
steam  admitted  up  to  cut-off  in  the  first  cyhnder  of  a  mul- 
tiple expansion  engine  has  increased  in  volume  up  to  release 
in  the  last  cylinder. 

If  the  release  be  considered  to  come  at  the  end  of  the 
stroke  the  number  of  expansions  for  any  engine  may  be  cal- 
culated from  the  diameter  of  the  cylinders  and  the  per  cent 
of  cut-oif  in  the  first  cylinder. 

Thus  —  cylinders  of  a  triple  engine  are  9" —  16"  —  24" 
X  30"  sti"oke ;  cut-ofE  at  ^  stroke  in  liigh  pressure  cyhnder. 

As  the  strokes  are  the  same  on  all  the  cylinders  of  this 
engine  the  volmnes  of  the  cylinders  Avill  be  as  the  squares  of 
their  diameters. 

If  the  high  j)ressure  cylinder  took  steam  to  the  end  of  its 
stroke  the  number  of  expansions  would  be  -gi'.  but  the  steam 
expands  tlu'ee  times  in  the  high,  so  the  total  expansion  in 
the  engine  is  ^^^  X  3  =  21.3. 

Sensible  heat  is  the  temperature  of  any  body,  as  air, 
water,  or  steam,  which  may  be  measured  by  the  thermometer. 

SpecifTG  heat  is  the  quantity  of  heat  required  to  raise  one 
unit  of  weight  of  the  substance  through  one  degree  of  tem- 
perature, measured  in- thermal  units. 


12  TECHNICAL  TERMS 

The  unit  of  heat,  or  thermal  unit,  is  the  quantity 
of  heat  required  to  raise  the  temj)erature  of  one  pound 
of  water  from  62°  to  63°  F.  This  is  often  called  the 
British  Thermal  Unit  (written  B.  t.  u.),  to  distingiiish 
it  from  the  German  and  the  French  standard,  which  is 
larger. 

Mechanical  equivalent  of  heat.  It  has  been  found  by 
experiment  that  if  one  pound  of  pure  water  at  62°  F.  be 
raised  to  63°  F.,  energy  is  exerted  equivalent  to  lifting 
seven  hundred  and  seventy-eight  (778)  pounds  one  foot  high, 
or  one  pound  seven  hundred  and  seventy-eight  (778) 
feet  high.  This  energy  is  called  the  inechanical  equivalent 
of  one  therntial  unit  of  heat,  and  it  is  usually  designated 
by  the  letter  J,  and  its  reciprocal  or  yi^  by  A. 

Saturated  steam.  When  steam  is  formed  in  a  closed 
vessel  in  contact  with  its  own  liquid,  it  is  said  to  be  satu- 
rated and  it  will  have  a  certain  definite  pressure  and  den- 
sity corresponding  to  each  different  temperature.  If,  at  the 
same  time,  the  steam  contains  no  liquid  in  susjiension,  it  is 
said  to  be  dry  and  saturated. 

Superheated  steam.  If,  after  all  the  liquid  has  been 
converted  into  steam,  more  heat  be  added,  the  tenq)erature 
will  rise  and  the  steam  is  said  to  be  superheated,  because  its 
temperature  will  l»e  greater  than  that  corresponding  to 
saturated  steam  of  the  same  2)>'<issure.  This  difference  is 
the  number  of  degrees  of  superheat. 

Priming.  It  is  possible  for  saturated  steam  to  hold 
particles  of  water  in  suspension.  The  steam  is  then  said  to 
be  primed  or  wet.  The  amount  of  water  so  suspended  may 
vary  from  zero  to  5  per  cent.  Ahnost  all  boilers  in 
which  the  steam  is  not  in  contact  with  the  hot  gases  give 
steam  primed  from  0.1  per  cent  to  3  per  cent. 

Thermal  efficiency  of  an  enyine.  An  engine  having  a 
thermal  efficiency  of  100  per  cent  would  reipiire  ^jj^*^  = 
42.42  B.  t.  u.  per  H.  P.  jier  minute.     An  engine  wliich  used 


TKCHXIOAI.    TERMS  13 

250  B.  t.  u.  per  H.  P.  per  mimite  tlius  has  a  thermal  etti- 
ciency  of  Vj^"  =  0.1(39,  or  16.9  per  cent. 

Mechanical  efficle)icy  of  an  engine.  This  is  the  ratio 
of  the  power  delivered  at  the  fly-wheel  or  shaft  to  that  cal- 
culated from  the  indicator  cards.  This  ratio  may  be  about 
90  per  cent. 

Temperature.  There  are  a  number  of  different  ther- 
mometric  scales.  The  Fahrenheit  and  the  Centigrade  ai-e 
the  two  most  generally  used.  In  the  Fahrenheit  system 
melting  ice  is  taken  as  32°,  and  boiling  water,  or  steam  at 
14.7  pounds  pressure,  is  taken  as  212°  F.  In  the  Centi- 
grade system  melting  ice  is  taken  as  0°  and  steam  at  14.7 
pounds  pressure  as  100°  C.  A  Centigrade  reading  may  be 
converted  into  the  Fahrenheit  scale  by  multiplying  the 
Centigrade  reading  by  |  and  then  adding  32.  The  zero  of 
each  of  these  two  systems  is  purely  arbitrary. 

It  is  possible  to  construct  a  thermodynamic  scale  of 
temperature  based  on  thermodynamic  laws.  The  zero  of 
this  scale,  called  the  absoiiite  zero,  is  459.5°  below  the  zero 
of  the  Falu'enheit  scale  and  273.1°  below  the  zero  of  the 
Centigi'ade  scale.  The  zero  obtained  by  wliat  is  known  as 
the  air  thermometer  agi'ees  very  closely  with  the  zero  of 
tlie  thermodynamic  scale.  The  absolute  temperature  corre- 
sponding to  100°  F.  is  100  +  459.5  =  559.5°. 

Ixothernuil  expansion.  If,  while  a  substance  expands, 
an  amount  of  heat  sufficient  to  keep  the  temperature  con- 
stant be  added,  the  expansion  is  said  to  be  isothermal.  The 
pressure  may  or  may  not  change  during  the  expansion.  In 
the  case  of  a  mixture  of  water  and  steam  the  pressure  would 
remain  constant  as  long  as  any  water  was  present.  In  the 
case  of  a  perfect  gas  the  pressui'e  would  decrease  in  the 
same  proportion  as  tlie  volume  increased. 

Isothernud  compression.  This  is  the  reverse  of  the  ex- 
pansion, and  heat  has  to  be  abstracted  during  compression 
in  order  to  keep  the  temperature  constant.     An  amount  of 


14  TKCHNICAL  TKKMS 

work  has  to  be  done  on  the  vapor  or  substance  in  compres- 
sing it  equal  to  that  which  would  be  obtained  as  useful 
work  during  an  isothermal  expansion  between  the  same 
limits. 

Adiahatic  expansion.  A  reversible  adiabatic  expansion 
is  such  an  expansion  as  would  take  place  between  cut-off 
and  release  in  a  steam  engine  or  compressed  air  engine,  if 
there  was  no  heat  given  to  or  taken  from  the  metal  form- 
ing the  cylinder  and  the  piston.  It  is  an  expansion  during 
wliich  no  heat  is  either  added  or  taken  away  as  heat.  As 
work  is  done  on  the  piston  it  must  be  paid  for  in  some  way. 
This  work  comes  from  the  internal  energy  the  substance 
had  at  the  beginning  of  the  expansion,  and  if  during  the 
expansion  7,780  foot-pounds  of  external  work  or  useful 
work  Avere  done  on  the  piston,  then  the  internal  energy  at 
the  end  of  this  expansion  would  be  7,780  foot-pounds  less 
than  at  the  beginning. 

During  an  adiabatic  expansion  lioth  the  jjressure  and  the 
temperature  drop  as  the  volume  increases.  If  the  sub- 
stance, when  compressed  adiabatically,  goes  back  over  the 
same  path  along  which  it  expanded,  the  expansion  or  com- 
pression takes  place  at  constant  entropy. 

Entropij  is  the  name  given  to  a  term  representing  the 
value  of  a  ratio,  or  the  value  of  the  summation  of  a 
number  of  such  ratios.  This  term  appears  frequently  in 
the  calculation  of  engineering  problems.  An  example  will 
illustrate.  Suppose  a  gas  to  expand  at  a  constant  tempera- 
ture of  100°  F.,  and  that  during  this  expansion  5  B.  t.  u.  are 

5 
added.    The  increase  in  entropy  is =  0.0089,  and 

^  -^        100  +  450.5 

is  found  by  dividing  the  heat  added  by  the  constant  abso- 
lute temperature  at  which  it  was  added. 

Suppose  that  instead  of  the  teniperature  remaining  con- 
stant, the  temperature  increased  10°  while  the  5  B.  t.  u.  were 
being  added.     An  approximation  to  the  increase  in  entropy 


TECHNICAL  TERMS  15 

could  be  made  as  follows  :  Each  heat  unit  caused  an  increase 
in  temperature  of  2°,  so  that  the  average  absolute  tem- 
perature, Avhile  the  first  heat  unit  was  being  added,  was 
101  +  459.5  =  560.5°.     The  increase  in  entropy  due  to  this 

one  heat  unit  is  approximately ;  the  increase  due    to 

560.5 

the  addition  of  the  second  heat  unit  at  an  average  absolute 

temperature  of  562.5  is ,  and  the  total  increase  is  ap- 

^  562.5  '  ^ 

proximately    e(iual     to    the     smn    of 1 1 

"^  56U.5        562.5        5(>4.5 

-\ 1 .     This  amount  is  smaller  than  in  the  case 

566.5       568.5 

where  the  temperature  remained  constant.  To  get  the  cor- 
rect value  of  the  increase  in  entropy  for  this  case,  we  should 
liave  a  summation  of  a  great  many  terms,  adding,  instead 
of  one  heat  unit,  an  infinitesimal  amount  of  heat  each  time, 
and  then  di\ading  each  infinitesimal  amount  of  heat  by  the 
absolute  temperature  at  which  it  was  added. 

It  is  evident  that  entropy  is  always  figured  as  the  increase 
or  the  decrease  between  two  conditions.  In  other  words, 
there  is  no  zero  entropy. 


CHAPTER  II 
THE  CROSBY  STEAM  ENGINE  INDICATOR 

The  Crosby  Steam  Engine  Indicator  is  designed  and 
constructed  to  meet  the  exacting  requirements  of  modern 
steam  engineering.  During  the  last  few  years,  under  tlie 
keen  search  and  exhaustive  tests  of  eminent  engineers,  the 
practice  in  this  department  of  science  has  undergone  impor- 
tant changes,  tending  to  estabUsh  more  correct  methods  and 
thereby  to  reach  more  accurate  results  ;  especially  is  this 
true  in  the  use  and  scope  of  the  indicator,  so  that  the  work 
done  with  such  instruments  in  former  times  seems  coarse 
and  crude  when  compared  with  the  more  exact  attainment 
of  the  present. 

Educators  in  the  scientific  schools  of  botli  Euro])e  and 
America  have  seen  the  importance  of  more  exact  knowledge 
and  instruction  in  the  technical  sciences ;  and  the  great 
achievements  of  recent  years  in  the  construction  of  build- 
ings, ships,  armaments  and  macliines  attest  the  thoroughness 
with  which  research  in  tliese  departments  has  been  pi'ose- 
cuted  ;  in  none  has  there  been  greater  progress  made  than 
in  mechanical  and  steam  engineering. 

A  knowledge  of  these  facts  has  kept  us  on  the  alert  in 
the  manufacture  of  all  our  steam  appliances,  and  especially 
in  that  of  the  steam  engine  indicator.  Within  a  recent 
time  we  have  made  important  improvements,  which,  as  we 
believe,  place  it  far  in  advance  of  any  other  instrument  of 
its  kind.  Radical  changes  in  design,  more  perfect  me- 
chanical construction,  due  to  the  use  of  improved  and 
specialized  machinery,  and  careful  selection  of  metals  for 
the  different  parts,  have  all  contributed  to  this  favorable 
result. 

16 


THE  CROSBY  STANDARD  INDICATOR 


17 


Tlie  movements  of  piston  and  pencil  ])oint  are  pevtectly 
parallel,  the  movement  of  the  pencil  point  is  also  exactly 
parallel  with  the  axis  of  the  drum.  This  accuracy  is 
secured  hy  mathematically  correct  design  and  careful 
workmanship. 


"k—iiiiJ 


The  rating  of  the  springs  hy  our  newly  constructed  test- 
ing apparatus,  which  emhodies  all  the  valualde  aids  to 
exactness  which  have  yet  heen  discovered,  is  nearer  perfec- 
tion than  could  have  heen  attained,  or  even  expected,  until 
within  a  very  recent  time. 


18  DESCRIPTION  OF  THE  INDICATOR 

CROSBY  STANDARD  STEAM  ENGINE  INDICATOR 

The  illustration  on  page  19  shows  the  design  and  arrange- 
ment of  its  parts. 

The  cylinder,  4,  in  which  the  piston  moves,  is  made  of 
a  special  alloy,  exactly  suited  to  the  varying  temperatures 
to  which  it  is  subjected,  and  secures  to  the  piston  the  same 
freedom  of  movement  with  high  pressure  steam  as  with  low  ; 
and  as  its  bottom  end  is  free  and  out  of  contact  with  all 
other  parts,  its  longitudinal  expansion  or  contraction  is 
unimpeded,  and  no  distortion  can  possibly  take  place. 

Between  the  cylinder,  4,  and  the  casing,  5,  is  an  annular 
chamber,  which  serves  as  a  steam  jacket ;  and  being  open  at 
the  bottom,  can  hold  no  water,  but  will  always  be  filled  with 
steam  of  nearly  the  same  temperature  as  that  in  the  cyhnder. 

The  ■pi^^ion-i  8,  is  formed  from  a  solid  piece  of  the  finest 
tool  steel.  Its  shell  is  made  as  thin  as  possible  consistent 
with  proper  strength.  It  is  hardened  to  prevent  any  reduc- 
tion of  its  area  by  wearing,  then  ground  and  lapped  to  fit 
(to  the  twenty-thousandth  part  of  an  inch)  a  cylindrical 
gage  of  standard  size.  Shallow  channels  in  its  outer  sur- 
face provide  a  steam  packing,  and  the  moisture  and  oil 
wliich  they  retain  act  as  lubricants,  and  prevent  undue  leak- 
age by  the  piston.  The  transverse  web  near  its  center  sup- 
ports a  central  socket,  which  projects  both  upward  and 
downward  ;  the  upper  part  is  threaded  inside  to  receive  the 
lower  end  of  the  piston-rod.  The  upper  edge  of  this  socket 
is  formed  to  fit  nicely  into  a  circular  channel  in  the  under 
side  of  the  shoulder  of  the  piston-rod,  when  they  are  prop- 
erly connected.  It  has  a  longitudinal  slot,  Avliich  permits 
the  straight  portion  of  wire  at  the  bottom  of  the  spring, 
vrith  its  bead,  to  drop  to  a  concave  bearing  in  the  upper  end 
of  the  piston-screw,  9,  which  is  closely  threaded  into  the 
lower  part  of  the  socket ;  the  head  of  this  screw  is  hexag- 
onal, and  may  be  turned  with  the  hollow  wTench  which 
accompanies  the  indicator. 


DKvSCBIPTION   OF  TUK  IKDICATOB 


19 


The  jyiston-rod ,  10,  is  of  steel,  and  is  made  hollow  for 
lightness.  Its  lower  end  is  threaded  to  screw  into  the 
upper  socket  of  the  piston.  Above  the  tlu'eaded  portion  is 
a  shoulder  having  in  its  under  side  a  circular  channel 
formed  to  receive  the  upper  edge  of  the  socket,  when  these 


parts  are  connected  together.  When  making  this  connec- 
tion be  sure  that  the  piston-rod  is  screwed  into  the  socket  as 
far  as  it  will  go,  that  is,  until  the  upper  edge  of  the  socket 
is  brought  firmly  against  the  bottom  of  the  channel  in  the 
piston-rod,  before  the  piston-screw,  9,  is  tightened  against  the 


20  DESCRIPTION  OF  THE  INDICATOR 

l)ea(l  at  the  foot  of  the  spring.  This  is  very  important,  as  it 
insures  a  correct  aUgnnient  of  the  parts  and  free  movement 
of  the  piston  within  the  cyhnder. 

The  swivel  head,  11,  is  threaded  on  its  lower  half  to 
screw  into  the  piston-rod  more  or  less,  according  to  the 
required  height  of  the  atmospheric  line  on  the  diagram. 
Its  head  is  pivoted  to  tlie  piston-rod  link  of  the  pencil 
mechanism.  This  adjustment  of  the  position  of  the  dia- 
gram upon  the  card  is  a  valuable  advantage  peculiar  to  the 
Crosby  indicator. 

The  cap,  2.  rests  on  top  of  the  cylinder,  and  holds 
the  sleeve  and  all  connected  parts  in  place.  It  has  a  cen- 
tral depression  in  its  upper  surface,  also  a  central  hole, 
furnished  with  a  hardened  steel  bushing,  which  serves  as  a 
very  durable  and  sure  guide  to  the  piston-rod.  It  projects 
downward  into  the  cylinder  in  two  steps,  having  different 
lengths  and  diameters  ;  both  these  and  the  hole  have  a  com- 
mon center.  The  lower  and  smaller  projection  is  screw- 
threaded  outside  to  engage  with  the  like  threads  in  the  head 
of  the  spring,  and  hold  it  Urndy  in  place.  The  upper  and 
larger  projection  is  screw-threaded  on  its  lower  half  to 
engage  with  the  light  threads  inside  the  cylinder ;  the  up})er 
half  of  this  larger  projection  —  being  the  smooth,  vertical 
portion  —  is  accurately  fitted  into  a  corresponding  recess  in 
the  top  of  the  cylinder,  and  forms  thereby  a  guide  by  which 
all  the  moving  paits  are  adjusted  and  kept  in  correct  align- 
ment, which  is  very  important  but  practically  impossible  to 
secure  by  the  use  of  screw  threads  alone. 

The  sleeve,  3,  surrounds  the  upper  part  of  the  cylinder 
in  a  recess  formed  for  that  purpose,  and  supports  the  pencil 
mechanism  ;  the  arm,  X,  is  an  integral  part  of  it.  It  turns 
around  freely,  and  is  held  in  place  by  the  cap.  The  handle 
for  adjusting  the  pencil  point  is  threaded  through  the  arm, 
and  being  in  contact  with  a  stop-screw  in  the  plate,  1,  may 
be  delicately  adjusted  to   the  surface  of  the  paper  on  the 


DESCRIPTION  OF  THE  INDICATOR  21 

drum.  It  is  made  of  hard  wood  with  a  lock-nut  to  main- 
tain the  adjustment. 

The  pencil  mechanism  is  designed  to  afford  sufficient 
strength  and  steadiness  of  movement,  with  tlie  utmost  liglit- 
ness ;  tliereby  eliminating  as  far  as  possible  the  effect  of 
momentum,  which  is  especially  troublesome  in  high  speed 
work.  Its  fundamental  kinematic  principle  is  that  of  the 
pantograph.  The  fulcrum  of  the  mechanism  as  a  whole, 
the  point  attached  to  the  piston-rod,  and  the  pencil  point  are 
always  in  a  straight  line.  This  gives  to  the  pencil  point  a 
movement  exactly  parallel  with  that  of  the  piston.  The 
mechanism  is  theoretically  correct  as  well  as  mechanically 
accurate  ;  the  result  is,  therefore,  mathematical  precision  in 
the  pencil  movement,  not  merely  an  approximation.  The 
movement  of  the  spring  throughout  its  range  bears  a  con- 
stant ratio  to  the  force  applied ;  and  the  amount  of  the 
movement  of  the  piston  is  multiplied  six  times  at  the  pencil 
point.  The  pencil  lever,  links,  and  pins  are  all  made  of 
hardened  steel ;  the  latter  —  slightly  tapering  —  are  ground 
and  lapped  to  fit  accurately,  without  perceptible  friction  or 
lost  motion. 

Springs.  In  order  to  obtain  a  correct  diagram,  the 
height  of  the  pencil  of  the  indicator  must  exactly  represent 
in  pounds  per  square  inch  the  pressure  on  the  piston  of  the 
steam  engine  at  every  point  of  the  stroke  ;  and  the  velocity 
of  the  surface  of  the  drum  must  bear  at  every  instant  a  con- 
stant ratio  to  the  velocity  of  the  piston.  These  two  essen- 
tial conditions  have  been  attained  to  a  greater  degree  of 
exactness  in  the  Crosby  indicator  than  in  any  other  make, 
by  a  very  ingenious  construction  and  nice  adaptation  of  both 
its  piston  and  drmii  springs. 

The  piston  spring  is  of  unique  and  ingenious  design, 
being  made  of  a  single  piece  of  the  finest  spring  steel  wire, 
wound  from  the  middle  into  a  double  coil,  the  ends  of  which 
are  screwed  into  a  metal    head    having    four  radial  wings 


22 


DESCRIPTION  OF  THE  INDICATOR 


drilled  helically  to  receive  and   hold   the  spring  securely  in 
place. 

Adjustment  is  made  hy  screwing  the  ends  into  the  head 
more  or  less,  until  exactly  the  right  strength  of  spring  is 
obtained,  when  they  are  there  firmly  fixed.  This  method 
of  adjusting  and  fastening  removes  all 
danger  of  loosening  coils,  and  obviates 
all  necessity  for  grinding  the  wires  —  a 
practice  fatal  to  accuracy  in  indicator 
S2)rings. 

The  foot  of  the  spring  —  in  which 
freedom  and  lightness  are  of  great  im- 
portance, it  being  the  part  subject  to  the 
greatest  movement  — ^  is  a  small  steel 
bead,  firmly  "  staked  "  on  to  the  wire. 
This  takes  the  place  of  the  heavy  brass 
foot  used  in  other  indicators,  and  reduces 
the  inertia  and  momentum  at  this  point 
to  a  minimum,  whereby  a  great  improve- 
ment is  effected.  This  bead  has  its  bearing  in  the  center  of 
the  piston,  and  in  connection  with  the  lower  end  of  the 
piston-rod  and  the  upper  end  of  the  piston-screw,  9  (both  of 
which  are  concaved  to  fit),  it  forms  a  ball  and  socket  joint 
which  allows  the  spring  to  yield  to  pressure  from  any  direc- 
tion without  causing  the  piston  to  bind  in  the  cylinder, 
which  occurs  when  the  sjjring  and  piston  are  rigidly  united. 
Designing  the  spring  so  that  any  lateral  movement  it  may 
receive  when  being  compressed  shall  not  be  conmmnicated 
to  the  piston  and  cause  errors  in  the  diagram,  is  of  extreme 
importance.      See  also  page  59. 

The  dnirn  spring,  31,  in  the  Crosby  indicator  is  in  form 
a  heUx,  while  in  other  indicators  it  is  a  long  volute.  It  is 
obvious  from  the  large  contact  surfaces  of  a  long  volute 
spring  that  its  friction  would  be  greater  than  that  of  a  short, 
open  helical  form  of  like  power ;    and  that  in  a  spring  of 


DESCRIPTION- OF  THE  INDICATOR  23 

this  kind,  for  a  given  amount  of  compression — as  in  the  move- 
ment of  an  indicator  drum  —  the  recoil  will  be  greater  and 
exerted  more  quickly  in  the  helical  than  in  the  volute  form. 

If  the  conditions  under  which  the  drum  spring  operates 
be  considered,  it  will  readily  be  seen  that  at  tlie  beginning 
of  the  stroke,  when  the  cord  has  all  the  resistance  of  the 
drum  and  spring  to  overcome,  the  spring  should  offer  less 
resistance  than  at  any  other  time  ;  and  at  the  beginning  of 
the  stroke  in  the  opposite  direction,  when  the  spring  has  to 
overcome  the  inertia  and  friction  of  the  drum,  its  energy  or 
recoil  should  be  greatest. 

These  conditions  are  fully  met  in  all  Crosby  indicators,  the 
drum  spring  being  a  helix  having  no  friction,  a  quick  recoil, 
and  scientifically  proportioned  to  the  work  it  has  to  do.  At 
the  beginning  of  the  forward  stroke  it  offers  to  the  cord 
only  a  very  slight  resistance,  which  gradually  increases  until 
at  the  end  its  maximum  is  reached.  At  the  beginning  of 
the  stroke  in  tlie  other  direction,  its  recoil  is  greatest  at 
the  moment  when  it  is  most  needed,  and  gradually  de- 
creases as  the  work  it  has  to  do  decreases,  until  at  the  end 
of  the  stroke  it  is  redxiced  to  its  minimum  again.  Thus, 
by  a  most  ingenious  balancing  of  opposing  forces,  the  most 
nearly  uniform  stress  on  tlie  cord  is  maintained  throughout 
each  revolution  of  the  engine. 

The  drum.,  24,  and  its  appurtenances,  except  the  drum 
spring,  are  similar  in  design  and  function  to  like  parts  of 
any  indicator,  and  need  not  be  particularly  described.  All 
the  moving  parts  are  designed  to  secure  svifficient  strength 
with  the  utmost  lightness,  by  whicli  the  effect  of  inertia  and 
momentimi  is  reduced  to  the  least  possible  amount.  It  is 
ordinarily  1^  inches  in  diameter,  this  being  the  correct  size 
for  high  speed  work,  and  answering  equally  well  for  low 
speeds.  If,  however,  the  indicator  is  to  be  used  only  for 
low  speeds,  and  a  longer  diagram  is  preferred,  it  can  be 
furnished  with  a  2  inch  drum. 


24 


CROSBY  NKW  INDICATOR 


All  Crosby  indicators  (except  some  of  the  Standard  Steam 
Engine  Indicators  numbered  below  3737)  can  be  readily 
changed  from  right-hand  to  left-hand  instruments  as  occa- 
sion may  re(|uire. 


CROSBY  NEW  STEAM  ENGINE  INDICATOR 

Patented 


This  instrimient  is  a  departure  from  the  ordinary  steam 
engine  indicator.  One  difference  is  in  the  location  of  the 
spring,  which  is  of  the  same  form  and  construction  as  the 
one  described  and  illustrated  on  page  22.  Tliis  has  been 
removed  fi'om  the  inside  of  the  cylindrical  case  near  the 
piston  to  the  outside  and   affixed  above  the  moving  parts, 


CROSBY  XKW  INDICATOR 


9r, 


where  it  will  remain  cool  under  all  conditions  of  use. 
Whatever  error  arises  from  heat,  therefore,  as  affecting  the 
spring  in  the  ordinary  indicator,  is  not  present  in  this 
instrmnent. 


The  other  and  more  important  difference  lies  in  the  size 
and  shape  of  the  piston.  This  piston  is  one  s(piare  inch  in 
area,  and  is  in  form  the  central  zone  of  a  sphere.  This 
increased  area  of  the  piston  provides  great  active  force  with 
a  very  light  pencil  mechanism.  It  is  attached  hy  a  rod 
directly  to  the  uj)per  part  of  the  spring,  and  moves  freely 


26  CROSBY  NEW  INDICATOR 

and  without  restraint  notwithstanding  there  may  be  eccen- 
tricity in  the  action  of  the  spring.  In  other  words,  this 
piston  serves  as  a  universal  joint  to  take  care  of  the  torsional 
sti'ains  of  the  spi'ing  when  it  operates  the  pencil  mechanism 
of  the  indicator.  The  pencil  mechanism  is  connected  to  the 
piston  by  means  of  a  rod  having  at  its  lower  end  a  ball, 
which  fits  into  a  socket  in  the  center  of  the  piston.  This 
socket  is  formed  upon  a  headless  slotted  screw,  adjustable 
in  the  piston,  by  which  it  is  possible  to  take  up  all  wear 
upon  the  ball  joint  that  might  develop  after  long  service ; 
l»ut  this  adjustment  should  not  ordinarily  be  disturbed,  and 
care  must  always  be  taken  to  insure  that  the  piston  is 
firmly  screwed  to  the  piston-rod  before  the  adjustment 
screw  is  tightened  to  just  the  amount  sufiicient  to  prevent 
any  possibility  of  lost  motion,  without  binding.  The  socket 
at  the  upper  end  of  the  piston-rod,  to  receive  the  ball  bear- 
ing of  the  spring,  is  likewise  upon  an  adjustable  headless 
screw,  which  is  independent  of  the  screw  beneath  it  that 
secures  the  swivel  head  of  the  piston-rod  in  its  place. 

The  piston-rod  moves  freely  within  a  sleeve  attached  to 
the  base  of  the  pencil  mechanism,  and,  moving  in  a  vertical 
line,  compels  the  pencil  to  move  also  in  a  vertical  line. 
Thus,  any  motion  of  the  piston  due  to  the  movements  of  the 
spring,  which  causes  the  spring-rod  to  deviate,  wiD  not  affect 
the  pencil  mechanism  in  its  vertical  course.  The  contact  of 
the  piston  with  the  interior  side  of  the  cylinder  is  a  line,  and 
does  not  induce  friction.  Ordinarily,  the  piston  of  an  indi- 
cator is  a  short  cylinder  fitted  to  shde  easily  within  another 
cylinder.  Such  a  piston  is  usually  about  one-half  inch  long, 
and  in  use  will  develop  friction  throughout  its  circumference. 
The  piston  so  made  must  resist  and  overcome  if  possible 
the  eccentricities  of  the  spring  in  action.  Yet,  even  then, 
there  is  always  a  want  of  freedom,  notwithstanding  there 
are  devices  to  aid  the  piston  in  such  case.  This  condition 
tending  to  error  is  recognized  by  engineers,  and  considered 


CROSBY  NEW  INDICATOR  XO.  2  27 

in  the  computations  made  of  the  diagram  taken  by  the  in- 
dicator. The  freedom  of  the  piston  movement  in  this  indi- 
cator dispenses  with  the  necessity  of  this  correction.  When 
an  indicator  is  to  be  used  in  higlily  superheated  steam  or  in 
gases  of  high  temperature  this  type,  with  outside  spring, 
will  give  accurate  results. 

All  parts  of  the  indicator  are  constructed  to  give  the 
greatest  possible  wear  and  durability  with  extreme  lightness 
and  freedom  from  all  friction  and  the  joints  are  upon  har- 
dened taper  bearings.  Means  are  thus  provided  to  prevent 
all  error  or  looseness,  and  no  proper  excuse  exists  for  per- 
mitting any  inaccuracy  to  develop.  Although  the  adjust- 
ment is  rarely  needed  and  at  every  point  is  slight  and 
simple,  greater  satisfaction  will  result  if  this  work  be  done 
by  skilled  mechanics  whose  special  experience  enables  them 
to  work  accurately  and  quickly,  wnthout  the  risk  of  dam- 
age involved  in  repairs  undertaken  by  persons  unfamiliar 
with  such  mechanism. 

This  indicator  is  made  also  for  gas  engine  work  with 
piston  1-  square  inch  in  area  and  special  pencil  mechanism ; 
and  may  be  made  of  steel  when  required,  for  ammonia. 

The  Crosby  New  Indicator  appeals  to  the  discriminating 
engineer  because  of  its  acknowledged  supeinority  in  design 
and  workmanship,  affording  unapproachable  accuracy  in 
results.  The  linkage  is  a  true  parallel  motion,  and  the 
relationship  of  the  parts  is  not  disturbed  when  changing  the 
spring  or  cleaning  the  cylinder.  The  operation  and  adjust- 
ment of  the  indicator  in  use  is  simple  and  convenient. 

On  the  following  page  examples  are  shown  of  its  free- 
dom of  piston  movement,  being  reproductions  of  the  original 
test  cards  of  a  variety  of  springs. 

CROSBY  NEW  INDICATOR  NO.  2 

Patented 

This  instrument  has  been  designed  to  meet  the  demand 
for  an  accurate  and  trustworthy  instrument  of  the  outside- 


28 


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CROSHV  NKW   1M)I(  ATOR  NO.  2 


29 


s])riiig  t.yi)e,  .smaller  and  less  costly  than  the  Crosby  New 
Indicator,  bnt  containing  its  essential  features  of  design.  It 
is  convenient  to  handle  and  gives  accurate  and  satisfactory 
results.  The  pencil  mechanism  and  spherical  piston  are 
similar  to  those  which  give  such  superiority  to  the  Crosby 
New  Indicator,  bxit  the  piston  has  an  area  of  ^  scpiare  inch. 
This  Crosby  New  Indicator  No.  2  is  made  also  for  ammonia. 
For  gas  engine  work  the  piston  is  ^  square  inch  in  area. 
As  a  Combined  Gas  and  Steam  Engine  Indicator  it  has 
two  interchangeal)le  ])istons  j  and  ^  square  inch  in  area. 


THE  CROSBY  INDICATOR  WITH   DRUM  FOR  TAKING 
CONTINUOUS  DIAGRAMS 

I'ateuted 


30  DRUM  FOR  CONTINUOUS  DIAGRAMS 

The  cut  represents  the  Crosby  New  Steam  Engine  Indi- 
cator equipjjeil  vntlx  a  drum  for  taking  continuous  dia- 
grams. Tliis  drum  can  he  ap^jlit^d  to  any  indicator.  It  is 
designed  to  use  a  roll  of  paper  2  inches  Avide  and  12  feet 
long,  upon  wliich  the  operation  of  the  indicator  traces  a 
series  of  diagrams  which  will  continue  until  the  roll  is  ex- 
hausted, unless  interrupted  hy  the  operator.  The  roU  of 
])aper  is  located  within  an  opening  in  the  shell  of  the  drum, 
thence  the  paper  passes  around  the  outside  of  the  drum  and 
uaward  to  the  central  cylinder,  to  which  it  is  attached.  The 
central  cylinder  is  concentric  with  the  di'um,  and  after  the 
})aper  has  been  wound  upon  it,  may  be  withdrawn  through 
the  toj)  and  the  paper  easily  detached.  Upon  the  top  of  the 
drum  and  cooperating  with  the  central  cylinder  is  a  knurled 
head  loosely  attached  to  the  drum  spindle,  wliich  controls 
the  distance  between  the  diagi'ams  so  that  by  adjustment 
they  will  vary  in  number  from  6  to  100  per  foot  of  paper. 
Tliis  advantage  of  taking  any  number  of  diagrams  on  the 
roll  at  the  will  of  the  operator  is  of  importance,  as  he  will 
be  able  to  regulate  the  duration  of  the  test  to  the  speed  of 
the  engine  in  taking  a  less  or  greater  mimber  per  foot  of 
l^aper.  Tliis  feature  is  novel  and  is  an  improvement  over 
devices  for  taking  diagrams  of  tliis  character  where  the 
number  is  fixed  for  all  engine  sjjeeds  ;  for  it  enables  the 
operator  by  limiting  the  nmiiber  according  to  his  own  judg- 
ment more  easily  to  read  and  measure  the  diagrams  taken. 

The  demand  for  an  indicator  with  a  drum  for  continuous 
diagrams  has  been  stimulated  recently  by  its  use  in  rolUng 
mills,  and  in  other  industries  where  there  is  an  irregular 
load  on  the  steam  engine,  varying  rapidly  and  in  such  se- 
quence that  knowledge  of  its  continuous  work  could  not  be 
obtained  except  by  an  unbroken  series  of  diagTams,  extend- 
ing over  a  definite  time  of  greater  or  less  extent.  But  its 
usefulness  is  not  confined  to  such  conditions.  Its  applica- 
tion to  any  steam  or  gas  engine  will  afEord  abundant  exam- 


COXTIXUOUS  DIAGRAMS 


31 


Sections  of  Continuous  Diagrams  Taken  with  the  Crosby 
Indicator  from  Rolling  Mill  Engines 


32  PRUM  FOR  (  ONTINUOUS  DIAGRAMS 

pies  of  its  action,  continuously  or  intermittently  at  tlie  will 
or  convenience  of  the  engineer.  It  furnishes  recorded 
proof  of  such  operation  in  a  form  that  permits  one  diagram 
to  be  compared  with  another,  and  the  variations  during  a 
cycle  of  operations  to  he  intelligently  observed  in  the 
sequence  of  their  occurrence. 

The  examples  on  page  ol  reproduced  from  actual  diagrams 
taken  on  steam  engines  are  given  only  to  illustrate  the  fore- 
going statement.  Single  isolated  diagrams  can  also  be 
taken  as  wdth  the  ordinary  climn. 

THE  LANZA  CONTINUOUS   DIAGRAM   APPLIANCE 
WITH   CROSBY  INDICATORS 

Patented 

This  apparatus  for  taking  an  uninterrupted  record  of  the 
pressure  changes  occurring  in  any  compression  chamber  or 
in  the  cylinder  of  any  steam  engine,  pump,  or  internal  com- 
bustion engine,  is  a  device  for  accuratel}^  feeding  a  con- 
tinuous strip  of  paper  in  one  direction  at  velocities  strictly 
proportionate  to  the  varying  velocity  of  the  piston  or  pump 
plunger  through  as  many  consecutive  strokes  of  the  reciprocat- 
ing parts  as  may  be  desired. 

It  is  the  invention  of  Professor  Gaetano  Lanza,  Professor 
of  Theoretical  and  Applied  Mechanics,  Emeritus,  of  the 
Massachusetts  Institute  of  Technology. 

The  paper  is  drawn  forward  from  a  roll  and  wound  after- 
ward in  form  for  convenient  removal  and  study.  The  suc- 
cessive diagrams  or  pressure  records  are  not  overlapping  or 
deformed  in  any  way,  but  each  pressure  cycle  is  separately 
developed  in  its  true  proportions.  The  horse  power  and 
pressures  can  be  conveniently  measured  by  scale  or  plani- 
meter  and  the  actual  location  of  the  several  events  deter- 
mined. 

A  full  description  of  this  instrument  and  its  uses  is  given 
on  page  196,  in  the  Appendi.x. 


CHAPTER  III 

THE    CROSBY    GAS     ENGINE    INDICATOR.      THE    CROSBY 

COMBINED    GAS    AND    STEAM    ENGINE   INDICATOR. 

THE    CROSBY    AMMONIA    INDICATOR.      THE 

CROSBY    ORDNANCE     INDICATOR.      THE 

CROSBY     HYDRAULIC     INDICATOR 


CROSBY  STANDARD  GAS  ENGINE  INDICATOR 


The  increase  in  the  use  of  gas  and  of  gasohne  engines 
has  created  a  demand  for  an  acciu-ate  indicator  capable  of 

33 


34  CROSBY  COMBINED  INDICATOR 

withstanding  the  heat,  the  high  pressure,  and  the  shock 
which  result  from  the  explosions  in  the  cyhnder. 

The  Crosby  Standard  Gas  Engine  Indicator  designed  to 
meet  these  requirements  has  given  ^)erf act  satisfaction.  The 
piston  is  :^  of  a  square  inch  in  area  and  springs  made 
for  ^  inch  pistons  have  their  rating  doubled  when  used 
in  this  instrument.  Its  great  accuracy  and  durability  have 
been  fully  demonstrated,  and  its  method  of  construction 
leads  to  the  least  error  in  the  taking  of  such  diagrams. 

The  Crosby  New  Indicator  is  made  also  for  gas  engine 
work,  with  piston  ^  square  inch  in  area,  of  the  design 
described  on  page  25. 

CROSBY  COMBINED    GAS    AND    STEAM    ENGINE 
INDICATOR 

Patented 

This  indicator  is  for  use  either  with  the  steam  engine  or 
with  gas  or  oil  engines,  and  is  suppUed  with  two  pistons, 
either  of  which  can  be  fitted  separately  as  desired.  The 
piston  for  steam  is  ^  square  inch  in  area,  the  same  as  is 
used  with  the  Crosby  Standard  Steam  Engine  Indicator ; 
the  one  for  gas  or  oil  is  ^  square  inch  in  area. 

The  cylinder  is  of  special  construction  to  suit  the  respect- 
ive diameters  of  the  two  pistons. 

CROSBY  AMMONIA  INDICATOR 

Patented 

The  Crosby  Ammonia  Indicator  is  made  like  the  Crosby 
Standard  Steam  Engine  Indicator,  except  that  all  surfaces 
exposed  to  the  action  of  ammonia  are  of  steel.  The  Crosby 
New  Indicator,  having  the  outside  spring,  is  also  made  of 
steel  when  required  for  ammonia.  For  ammonia  indicators, 
both  common  and  three-way  (;ocks  are  made  of  steel. 


CROSBY  ORDXANCE  INDICATOR 

CROSBY  ORDNANCE  INDICATOR 

Patented 


35 


This  instrument  will  give  a  true  record  of  high  pressures, 
such  as  ohtain  in  the  operation  of  the  pneumatic  gun  car- 
riage for  heavy  ordnance,  or  in  hydraulic  pumps. 

The  pencil  mechanism  is  strong,  and  has  a  post  bearing 
lightly  against  the  ])encil  arm  to  keep  it  in  contact  with  the 
drum  during  sudden  shocks. 

The  piston  is  -^^  of  a  square  inch  in  area,  and  is  fitted  into 
a  cylinder  at  the  bottom  of  the  instrument.  There  is 
a  by-pass  by  wliich  the  pressure  may  be  transmitted  to  the 
larger  piston  above,  when  the  pressures  to  be  recorded  are 
not  too  high  for  the  capacity  of  the  spring.  This  by-pass 
is  closed  by  a  cock  when  the  small  piston  is  to  be  used. 


36  CROSBY  HYDRAULIC  IXDICATOR 

CROSBY  HYDRAULIC  INDICATOR 

Patented 

The  Crosby  Hydraulic;  Indicator  (litters  from  the  one 
shown  in  the  cnt  in  that  it  has  no  by-pass  and  in  })lace  of 
the  piston  in  the  upper  chamber  a  guide  is  substituted. 

It  is  a  strong  and  efficient  instrument  for  indicating  under 
liigh  pressure  conditions  in  all  liquids  or  gases.  The  piston 
is  -^Q  of  a  square  inch  in  area.  The  cylinder  is  constructed 
in  such  a  manner  as  to  afford  a  uniform  area  of  cross-section 
below  the  piston,  thus  preventing  pockets  or  enlargements. 
The  pencil  mechanism  is  substantial  and  without  appreciable 
inertia  effect. 


CHAPTER  TV 

INDICATOR  ATTACHMENTS  AND  ACCESSORY  APPARATUS 

SARGENT  IMPROVED  ELECTRICAL  ATTACHMENT 
For  Steam  or  Gas  Engine  Indicators 


Fig.  3 

In  making  elaborate  tests  of  power  plants,  it  has  hereto- 
fore been  necessary  to  employ  as  many  assistants  as  there 
were  intlicators  used,  but  the  difficulty  of  securing  simulta^ 
neous  action  on  their  part  is  so  great  that  satisfactory  work 
is  rarely  to  be  obtained,  and  more  certain  means  to  that  end 
are  now  considered  necessary. 

Mr.  Frederick  Sargent.  M.E.,  invented  and  patented  an 
electrical  device  applicable  to  an  indicator,  by  means  of 
which  any  number  of  instruments  can  be  operated  and  dia- 
grams taken  at  the  same  instant  of  time,  simply  by  closing 
an  electric  circuit.      We  are  the  sole  owners  of  this  patent 

37 


38 


SARGENT  IMPROVED  ATTACHMENT 


and  of  the  rights  under  it ;  and  are  the  sole  makers  of  tliis 
apparatus,  which  has  been  modified  and  improved. 


Fig.  4 


Fig.  3  shows  a  Crosby  Standard  Indicator  fitted  with  this 
electrical  attachment.  Fig.  4  shows  the  same  indicator 
fitted  Avith  a  Circuit  Closer. 

Description 
Fig.  5  represents  the  Sargent  Improved  Electrical  Attach- 
ment, consisting  of  an  electromagnet,  A,  which  is  supported 
by  a  bracket,  B,  wliich  also  secures  it  to  the  indicator  plate. 
Binding  posts,  C,  C,  are  attached  to  the  same  bracket.  The 
armature  D  is  opposed  to  the  magnet  by  a  spiral  spring  in 
the  center  of  the  coil,  the  tension  of  which  is  adjustable  by 
means  of  the  screw  E,  at  the  back  of  the  magnet.  The 
movement  of  the  armature  outwardly  is  limited  by  two 
screws,  1  and  2.  To  the  armature  is  secured  a  small  latch 
or  hook,  F,  which  is  free  to  work  vertically,  and  engage 
with  the  arm  A,  Fig.  3.  The  thumb-screw  G  is  for  fasten- 
ing the  attachment  to  the  plate  of  an  indicator  through  a 
hole  therein. 


TO  ATTACH  THE  ELECTRICAL  ATTACHMENT 


39 


Fig.  6  represents  the  Circuit  Closer,  and  is  designed  to 
operate  the  electrically  connected  indicators,  by  closing  the 
circuit  through  them  whenever  the  stylus  or  marking  point 
is  put  against  the  paper  on  the  drum  of  the  indicator  to 
wliich  it  is  attached.  This  enables  the  engineer  making  the 
test  to  control  this  indicator  directly  hy  hand  —  a  feature 
often  desirable  —  and  by  its  use  one  Sargent  attachment 
is  dispensed  with. 


It  consists  of  a  bracket,  H,  with  a  tubular  projection,  I, 
fastened  to  it  which  contains  the  circuit  closing  mechanism. 
It  is  attached  to  the  indicator  plate  by  the  thumb-screw,  J, 
in  precisely  the  same  way  that  the  magnets  are  to  the  other 
indicators,  and  is  electrically  connected  in  the  same  manner 
through  the  binding  posts,  K,  K. 


To  Attach  the  Sargent  Improved  Electrical  Attachment 

To  get  the  position  of  the  hole  in  the  frame  of  the  indi- 
cator, take  out  the  screw  G  (Fig.  ;">),  and  place  the  bracket 


40 


TO  ATTA<H  THE  CIROUTT  CLOSER 


liolding  the  magnet  against  the  plate  of  the  indicator,  so 
that  tlie  hook  F  (Fig.  5),  when  placed  horizontally,  will 
point  to  the  middle  of  the  arm  A  (Fig.  3)  ;  then  sci'ihe 
through  the  screw-hole  its  location  upon  the  plale  of  the 
indicator  ;  remove  tlie  attachment,  and  drill  a  hole  where 
marked  that  will  allow  the  screw  G  (Fig.  T))  to  i)ass  tlnough  it. 

Screw  the  attachment  to 
the  plate  and  adjust  it  so 
that  there  will  he  no  loose- 
ness, turning  the  screws 
M  M  (Figs.  5  and  6),  set- 
ting tliem  up  gently. 

Drop  the  hook  F  (Fig. 
5)  to  a  horizontal  position, 
and  bring  the  arm  A  (Fig. 
3)  up  to  its  working  po- 
sition, and  mark  on  it  the 
center  of  the  hole   to  he 
drilled    for    a    screw-eye. 
This    hole    should    he    so 
drilled  that  the  latch  will  stand  level  with  the  plate  when 
in  use.     The  size  of  the  hole  may  he  determined  from  the 
screw-eye  furnished. 

To  Attack  the  ClrcKit  Closev 

The  position  of  the  hole  in  the  indicator  plate  for  attach- 
ing the  Circuit  Closer,  Fig.  6,  is  determined  in  the  same 
manner  as  for  the  electromagnet,  taking  care  that  the  hut^ 
ton  L  (Fig.  6)  impinges  the  center  of  the  arm  A  (Fig.  4) 
when  the  sleeve  is  turned  into  the  correct  position  for  use. 

The  sleeve  handle  of  the  indicator  is  unscrewed  far 
enough  to  allow  the  button  L  (Fig.  6)  in  the  end  of  the 
projection  I  to  go  in  as  far  as  it  will,  then  the  marking 
point  must  lie  adjusted  until  it  makes  the  desired  tracing  on 
the  paper. 


Fig.  6 


TO  OPERATE  THE  ELECTRICAL  ATTACHMENT  41 

To  Operate  the  Sargent  Improved  Electrical  Attachment 
and  Circuit  Closer 

For  the  purpose  of  illustrating  the  manner  of  operating 
the  attaclmient,  assume  that  it  is  desirable  to  procure  simul- 
taneous diagrams  from  a  compound  engine,  taking  cards 
from  the  ends  of  each  cylinder.  Attach  the  indicators  to 
the  engine  and  arrange  the  dium  motion  in  the  usual  man- 
ner. On  each  indicator  secure  the  electrical  attaclunent  to 
its  plate  by  means  of  screw  G,  as  above  described.  Make 
the  connections  with  the  battery,  having  all  of  the  several 
magnets  and  the  circuit  closer  in  series.  Place  the  paper 
upon  the  drum,  and  l)ring  the  pencil  arm  into  such  a  posi- 
tion as  will  allow  the  latch  F  to  drop  into  the  screw-eye 
before  mentioned. 

Press  the  armature  firmly  against  the  magnet,  and  adjust 
the  marking  j)oint  to  the  ])ai)er  in  the  usual  manner.  The 
sleeve  handle  must  be  unscrewed  enough  to  allow  the  full 
operation  of  the  armature.  The  circuit  should  be  closed 
and  the  armature  tension  springs  adjusted,  so  that  the  con- 
nected attachments  will  work  simultaneously.  Everything 
shoidd  now  be  in  readiness  to  take  diagrams.  Connect  the 
drum  motions,  open  the  indicator  cocks,  and  as  soon  as  de- 
sirable close  the  circuit,  and  instantly  all  of  the  pencils  will 
be  brought  against  the  papers  and  \n\[  remain  there  as  long 
as  the  circuit  is  kept  closed. 

In  order  to  put  on  new  papers,  disengage  the  drum 
motions,  lift  the  latch,  and  swdng  the  pencil  arm  out  of 
the  way. 

The  Electric  Battery 

The  amount  of  battery  power  required  will  vary  with 
circumstances,  and  will  range  from  one  to  two  or  more  cells 
of  a  No.  2  Samson  l)attery,  or  its  equivalent. 

Tlie  batteiy  for  o])erating  the  attachments  is  enclosed  in 
a  neat  hardwood  l)ox  with  a  suitable  handle  for  carrying  it, 
and  is  sealed  so  as  to  prevent  slopping.      Tt  is  very  compact 


42 


CROSBY  DRUM  DETENT 


and  jjortable,  being  at  the  same  time  extremely  active,  long 
lived,  and  especially  adapted  to  open  circuit  work. 

The  connections  to  the  indicator  attachments  can  be  made 
with  the  battery  without  opening  the  box,  the  binding  posts 
being  on  the  outside. 

This  battery,  with  a  quantity  of  suitable  wire  for  making 
connections,  is  furnished  with  the  attachment. 


CROSBY  STANDARD  STEAM  ENGINE  INDICATOR 
WITH  2  INCH  DRUM  AND  DETENT 
,  Patented 


PLANIMETERS 


43 


The  detent  device  has  its  pawl  attached  to  the  base  plate 
of  the  indicator  and  is  j)rovided  with  a  suitable  handle  for 
operating  it.  The  pawl  engages  the  ratchet  located  at  the 
base  of  the  dinim.      See  also  page  73. 


PLANIMETERS 
With  Directions  for  Using  the  Planimeter  on  Indicator  Diagrams 


No.  1  Planimeter 

This  cut  represents  the  No.  1  planimeter.  It  is  the  sim- 
plest form  of  the  instrument,  having  but  one  wlieel,  and  is 
designed  to  measure  areas  in  square  inches  and  decimals  of 
a  square  inch.  The  figures  on  the  roller  wheel  D  represent 
units,  the  graduations  on  the  wheel  represent  fe//f/is,  and  the 
vernier  gives  the  hundredths. 


No.  2  Planimeter 


Tliis  cut  represents  the  No.  U  planimeter,  wliich  is  the 
same  as  the  No.  1,  with  the  addition  of  a  counting  disc  G, 
the  figures  on  which  represent  tens  and  mark  complete  revo- 
lutions of  the  roller  wheel.  By  this  means  areas  greater 
than  ten  square  inches  can  be  measured  with  facility.  The 
result  is  given  in  square  inches  and  decimals,  and  the  read- 
ing from  the  roller  wheel  and  vernier  is  tlie  same  as  with 
No.  1. 


44 


PLANIMETER  MECHANISM 


The  No.  3  planimeter  differs  somewhat  in  design  from  the 
two  previously  descrihed.      It  is  capable  of  measuring  larger 
areas,  and  by  means  of  the  adjustable  arm  A, 
giving  the   results   in   various   denominations  of 
value,   such  as  square  decimeters,   square   feet, 
and  square  inches  ;  also 
of    giving    the     average 
height    of    an    indicator 
diagram   in   fortieths  of 
an  inch,  which  makes  it 
a  very  useful  instrument 
in  connection  with  indi- 
cator work. 


Recordhig  Mechanism. 

Fig.  7  shows  in  detail 
the  recording  mechanism 
of  a  No.  3  planimeter, 
from  which  the  method 
of  reading  from  either 
instrument  may  be  easily 
understood.  G  is  the 
counting  disc,  1)  the 
roller  wheel,  and  E 
the  vernier.  From  the 
counting  disc  we  read 
1  (ten),  for  the  last 
figure    that    has    jiassed 


III 

-Ir 

MM 

lllli 

"1' 

!l 

0 

i 

«                \ 

1 

1 

Fig.  7 


DIRKCTIOXS  FOR  MEASURING 


45 


the  index  line  on  the  post  J  ;  from  the  roller  wheel  we 
read  4  (units),  for  the  last  figure  that  has  passed  zero  on 
the  vernier ;  we  also  read  7  (tenths),  for  that  nunil)er  of 
graduations  beyond  4  that  have  also  passed  zero  on  the 
vernier  (shown  by  the  dotted  line  a),  then  from  the  vernier 
we  reads  (hundredths),  because  the  third  graduation  on  the 
vernier  coincides  with  a  graduation  on  the  roller  wheel. 

The  complete  reading  will  then  be  14.73  square  inches. 

When  starting  from  zero  the  movement  of  the  counting 
disc  need  not  be  noted  when  measuring  single  indicator  dia- 
grams, as  they  are  of  less  than  ten  square  inches  area. 

Directions  for  Measuring  an  Indicator  Diagram 
ivith  a  No.  1  or  No.  2  Planimeter 

Care  should  l)e  taken  to  have  a  Hat,  even,  unglazed  sur- 
face for  tlie  roller  wheel  to  travel  upon.  A  slieet  of  dull 
finished  cardboard  serves  the  purpose  very  Avell. 


Fig.  8 


46  DIRECTIONS  FOR  USING  THE  PLAXIMETKR 

Set  the  weight  in  position  on  the  pivot  end  of  the  bar  P, 
and  after  placing  the  instrument  and  the  diagram  in  about 
the  position  shown  in  the  cut  (Fig.  8),  press  do\Vn  the  needle 
point  so  that  it  will  hold  its  place  ;  set  the  tracer  point  at 
any  given  point  in  the  outline  of  the  diagram,  as  at  F,  and 
adjust  the  roller  wheel  to  zero.  Now  follow  the  outline  of 
the  diagram  carefully  with  the  tracer  point,  moving  it  in  the 
direction  indicated  by  the  arrow,  or  that  of  the  hands  of  a 
watch,  until  it  returns  to  the  point  of  beginning.  The  result 
may  then  be  read  as  follows  :  Suppose  we  find  that  the  larg- 
est figure  on  the  roller  wheel  D,  that  has  passed  by  zero  on 
the  vernier  E,  to  be  2  (units),  and  the  nmnber  of  gradua- 
tions that  have  also  passed  zero  on  the  vernier  to  be 
4  (tenths),  and  the  number  of  the  graduation  on  the  vernier 
which  exactly  coincides  with  the  graduation  on  the  wheel 
to  be  8  (hundredths),  then  we  have  2.48  square  inches  as 
the  area  of  the  diagram.  Divide  this  by  the  length  of  the 
diagram,  which  we  will  call  3  inches,  and  we  have  .8266 
inches  as  the  average  height  of  the  diagram.  Multiply  tliis 
by  the  scale  of  the  spring  used  in  taking  the  diagram,  which 
in  this  case  is  40,  and  we  have  33.06  pounds  as  the  mean 
effective  j^ressure  per  square  inch  on  the  piston  of  the 
engine. 

Directions  for   Using  the  No.  3  Planimeter 

No.  3  planimeter  is  somewhat  differently  manipulated, 
although  the  same  general  principle  pertains.  The  figures 
on  the  wheels  may  represent  different  quantities  and  values 
according  to  the  particular  adjustment  of  the  sliding  arm  A. 
If  it  is  desired  merely  to  find  the  area  in  square  inches  of 
an  indicator  diagram,  set  the  sliding  arm  so  that  the  10^ 
inch  mark  will  exactly  coincide  with  the  vertical  mark  on 
the  inner  end  of  the  sleeve  H  at  K,  Fig.  7.  The  shding 
arm  is  released  or  made  fast  by  means  of  the  set-screw  S. 

With  the  wheels  at  zero  and  the  planimeter  and  diagram 


DIRECTIOXS  FOR  USLXG  NO.  3  PLAXIMETER 


47 


in  the  proper  position  (shown  in  Fig.  8)  trace  the  outhne 
carefully,  and  read  the  result  from  the  roller  wheel  and 
vernier,  the  same  as  directed  for  the  No.  1  and  No.  2 
instruments. 

Examplp :  Suppose,  in  a  diagi'am  so  measured,  we  read 
from  the  figures  on  the  roller  wheel  3  (units),  from  the 
graduations  on  the  roller  wheel  0  (tenths),  and  from  the 
vernier  8  (hundredths),  then  we  have  an  area  of  3.08  square 
inches  ;  to  find  the  average  height  we  divide  this  by  its 
length,  which  is  3^  inches.  Thus.  3.08 -j- 3.5=  0.88  of  an 
inch,  the  average  height.  This  multijilied  hy  the  scale  of 
the  spring  used,  which  in  tliis  case  is  60  pounds,  gives 
52.8  pounds  as  the  M.  ¥..  P. 


Fig.  9 

To  find  the  average  height  of  an  indicator  diagram  at  one 
measurement,  set  the  sliding  arm  so  that  the  steel  points  on 
its  upper  side  shall  be  just  the  length  of  the  diagram  — 
measured  on  a  hne  parallel  with  the  atmospheric  line  — 
apart,  as  shown  in  Fig.  9.  Withtliis  adjustment  the  figures 
on  the  counting  disc  represent  hundreds,  those  on  the  roller 
wheel  tens,  the  intermediate  gi-aduations  miits,  and  the 
vernier  gives  the  decimal.  Place  the  instrument  in  position 
^^^th  the  wheels  at  zero,  and  trace  the  outline  of  the  diagram. 
The  result  of  the  reading  -will  be  its  average  height  in  for- 
tieths of  an  inch. 


48  DIKKcrriONS  FOK  USINC  NO.  3   PLAXIMETER 

Kxam.ple:  Measuring  the  same  diagram  as  before,  sup- 
pose we  read  from  the  figures  on  the  roller  wheel  3  (tens), 
fi'om  the  graduations  5  (units),  and  from  the  vernier 
2  (tenths)  ;  then  we  have  ?>^. 2  fortieths  of  an  inch,  which, 
divided  l>y  40,  gives  0.88  of  an  inch,  the  average  height. 
This  multijjlied  hy  the  scale  of  the  spring  used  and  we 
have  52.8  pounds  M.  E.  P.,  the  same  as  in  the  last 
example.  A  simpler  process  is  to  multiply  the  reading  hy 
{\\efacto7'  corresponding  with  the  scale  of  the  spring,  which  for 
a  60  pound  spring  is  1.5,  then  we  have  35.2  X  1.5  =  52.8 
pounds,  the  same  as  by  the  other  process. 

FoUoAving  is  a  list  of  the  pressures  or  scales  to  which  in- 
dicator springs  are  commonly  made,  with  their  correspond- 
ing/"actons  immediately  below. 

Springs,  I   8    j  12  |  16     20     24  I   30      40  I  50   i  60  I  80  1 100   120    150  j  180 
Factors,  I  0.2  1  0.3  I  0.4  I  0.5  1  O.B  I  0.75    1.0    1.2511.5  I  2.0  I  2.5    3.0  1 3.751   4.5 

When  two  diagrams  are  taken  on  the  same  card  they  may 
be  measured  conjointly  and  the  average  height  divided  by 
two  to  get  the  average  height  of  Itoth.  We,  however,  recom- 
mend that  each  diagram  be  measured  separately,  especially 
if  there  is  a  difference  in  their  areas,  which  is  generally  the 
case. 

When  there  is  a  loop  in  the  diagram  caused  by  the  steam 
expanding  below  the  back  pressure  line  when  the  engine  is 
non-condensing,  its  outline  should  be  traced  in  the  same  way 
as  directed  for  a  plain  diagram,  as  the  principle  on  which 
the  planimeter  works  is  such  that  the  area  of  the  looji  will 
be  subtracted  fi-om  the  main  pai't  of  the  diagram,  and  the 
reading  of  the  instrument  when  the  measurement  is  com- 
pleted will  be  the  correct  net  area  sought. 

When  one  has  become  familiar  with  the  use  of  the  plani- 
meter it  is  not  necessary  always  to  set  the  wheels  at  zero,  as 
recpiired  in  the  foregoing  directions,  but  their  reading  as 
they  stand  just  before  beginning  to  trace  a  diagram   may  be 


THE  THR()TTLIX(t  CALORIMETER  49 

noted  down  and  this  quantity  subtracted  from  the  reading 
when  the  tracing  is  completed.  The  difference  between  the 
two  readings  is  the  area  sought. 

For  instance  :  Suppose  we  find  that  the  reading  of  the 
wheels,  including  the  counting  disc,  at  the  beginning  is 
47.31,  and  when  the  tracing  is  completed  it  is  49.43,  then 
49.43  —  47.31  =  2.12  square  inches,  the  area  measured. 
Then  to  measure  a  second  diagi-am,  note  down  the  last  read- 
ing, viz.,  49.43,  and  when  the  tracing  is  completed  we  read 
51.63.  Then  51.63  —  49.43  =  2.20  square  inches,  the  area 
of  the  second  diagram. 

The  foregoing  directions  for  using  the  planimeter  ai-e 
appli('al)le  to  any  single  diagram. 

The  use  of  Amsler's  Polar  Planimeter  in  the  measure- 
ment of  indicator  diagrams  enables  one  to  measure  ten  cards 
with  it  in  the  time  which  would  be  required  to  measure  one 
card  by  any  other  method,  and  it  insures  the  utmost  accuracy 
in  the  work. 

The  i)lanimeter  is  a  precise  and  delicate  instrument  and 
should  l)e  handled  and  kept  with  great  care,  in  order  that  it 
may  be  depended  upon  to  give  correct  results.  After  using, 
it  should  be  wiped  clean  with  a  piece  of  soft  chamois  skin. 

THE  THROTTLING  CALORIMETER 

In  order  that  the  test  of  an  engine  or  boiler  may  be  com- 
plete a  determination  should  be  made  of  the  quality  of  the 
steam,  i.e.,  the  j)rinung  or  the  amount  of  moisture  carried 
by  the  steam.  This  determination  was  formerly  made  by 
methods  wliich  could  be  made  to  give  satisfactory  results  in 
the  hands  of  a  physicist  or  a  trained  expert,  but  which  were 
troublesome  and  unreliable  when  enq)loye(l  by  an  inexpe- 
rienced observer.  The  quality  of  steam  delivered  by  a  boiler 
or  su])plied  to  an  engine  can  now  be  determined  with  ease 
and  certainty  l)y  aid  of  the  throttling  calorimeter,  invented 
by  Prof.  C.  H.  Peabody  of  the  JVIassachusetts  Institute  of 


50 


THK  THROTTLING  CALORIMKTER 


Technology,  and  described  hy  him  in  the  "  Journal  "  *  of 
the  Franklin  Institute,  and  in  the  "  Proceedings  of  the 
American  Society  of  Mechanical  Engineers."! 


Fi(!.  10 


The  throttling  calorimeter  depends  on  tlie  2)rinci})le  that 
steam  which  contains  a  moderate  amount  of  moisture  will 

*  "  Journal  "  Franklin  Institute.     June,  1888.     Volume  CXXVI.,  Page  1.34. 
t  "  Proceeding.s  American  Society  of  Mechanical  Engineers,"  1888-89,  Volume 
X.,  Page  327,  and  188'J-"J0,  Volume  XI.,  Page  193. 


THK  THROTTLIN(i  CAI.ORIMETER 


51 


become  su])erheate(l  if  the  pressure  is  reduced  by  tlu'ottling, 
without  loss  of  heat.  The  form  here  shown  is  simple, 
sul)stantial,  and  inexpensive,  and  has  been  used  by  the 
inventor  and  others  with  complete  satisfaction.  The  calorim- 
eter, shown  in  Fig.  10,  is  a  closed  cylindrical  metallic 
chamber  K,  having  an  inlet  passage  at  A,  controlled  by 
the  valve  E,  an  outlet  ])assage  at  the  bottom  N,  and  a  ther- 
mometer cup  at  T.  The  chamber  is  thickly  wrapped  with 
asbestos  and  hair  felt,  protected  by  wood  lagging  to  reduce 
radiation  and  loss  of  heat.  The  U  shaped  tubes  or  siphons 
for  attaching  the  pressure  gages  B  and  C  are  furnished  with 
the  calorimeter ;  the  gages  and  thermometer  are  extra,  and 
may  be  furnished  or  not,  as  required. 

The  nip])le  A,  connecting  the  inlet  valve  E  with  the 
chamber  K,  is  made  of  composition,  cut  with  pijje  thread 
and  provided  with  a  well  rounded  orifice  for  gaging  the  flow 
of  steam  as  shown  by  the  full  size  Fig.  11. 

The  connection  with  the  main  steam  pipe  from  which  a  sam- 
ple of  steam  to  be  tested  is  taken,  should  be 
as  short  and  direct  as  possible,  and  should 
be  well  wrapped  to  reduce  i-adiation.  The 
su])ply  pijte  should  enter  the  main  steam 
pi])e  at  least  half  an  inch,  when  the  con- 
nection is  made  on  the  up])er  side  of  the 
main.  If  the  calorimeter  is  attached  to 
the  bottom  half  of  the  main,  the  entering 
])ipe  should  extend  in  beyond  the  center. 
The  waste  pipe  N  should  be  at  least  one 
inch  in  diameter  for  its  entire  length,  and 
may  be  larger  if  longer  than  twenty  feet. 
The  gage  C  for  measuring  the  ])ressure  in 
the  main  steam  i)ipe  must  l)e  attaclied  di- 
rectly to  that  pipe  close  to  the  calorimeter. 

To  use  the  calorimeter,  fill  the  thermometer  cup  with 
oil    and    insert    the     thermometer ;     see    that    the    siphons 


Fig.  11 


52  THK  THROTTLING  CALORIMETER 

are  filled  with  cold  water  and  that  they  do  not  leak ; 
open  the  valve  E  wide,  and  wait  ten  or  fifteen  minutes  till 
the  whole  apparatus  is  heated.  Read  the  gage  B  and  add 
the  pressure  of  the  atmosphere*  to  get  the  ahsolute  pressure 
in  the  calorimeter ;  find  the  corresponding  temperature 
from  a  talde  of  the  properties  of  saturated  steam  and 
compare  with  the  temperature  in  the  calorimeter  given  l)y 
the  thermometer ;  the  excess  of  the  latter  over  the  former 
is  the  superheating  of  the  steam  in  the  calorimeter.  The 
flow  of  steam  through  the  calorimeter  will  he  sufficient  to 
make  the  loss  hy  radiation  of  no  consequence  and  no  cor- 
rection need  be  applied. 

When  all  is  ready,  read  the  pressure  of  the  steam  p 
in  the  main  steam  pii)e,  the  temperature  t^  in  the  calorim- 
eter, the  pressure  p^  in  the  calorimeter,  and  take  the  ])res- 
sure  y>„  of  the  atmosphere.  From  a  table  of  the  ])roperties 
of  saturated  steam,  find  the  temjierature  t^  corresponding 
to  the  absolute  pressure  P^  =  p^  +  Pa 

From  the  same  tables  find  the  total  heat  X^  corresponding 
to  the  pressure  P^ ;  also  the  heat  of  vaporization  /•  and  the 
heat  of  the  liquid  q  corresponding  to  the  ahsolute  pressure 
in  the  steam  pipe  Y  =  p  -\-  p^^ 

The  weight  or  moisture  in  1  pound  of  moist  steam  drawn 
from  the  steam  pipe  is  to  be  calculated  by  the  equation 

Prixning  =  1  -  K^^-^HU-t>-<l 

in  which  the  factor  0.48  is  the  specific  heat  of  su])erheated 
steam  at  constant  pressure. 

The  calculation  will  be  readily  understood  from  the  fol- 
lowing example : 

Pressure  in  steam  pipe,  p  =  69.8  pounds. 

Pressure  in  the  calorimeter,  p  =  12  pounds. 

*  Note.  The  pressure  of  the  atmosphere  is  commonly  assumed  to  be  14.7 
pounds  per  square  inch ;  it  may  be  taken  by  aid  of  a  barometer  or  obtained  from 
published  records  of  the  Weather  Bureau  for  the  day.  Inches  of  mercury  can  be 
reduced  to  pounds  per  square  inch  by  multiplying  by  0.49. 


THE  THROTTLIXG  CALORIMETER  53 

Pressure  of  the  atmosphere,  j^a  =  14.8  pounds. 

Temperature  in  the  calorimeter,  t^  =  268.2°  F. 

Absohite  pressure  in  steam  pipe,  P  =  ^9  +  p^^  = 
69.8  +  14.8  =  84.6  pounds. 

Absohite  pressure  in  calorimeter,  P^  =  p^  j^  p^  = 
12  +  14.8  =  26.8  pounds. 

Temperature  of  saturated  steam  at  26.8  pounds,  243.9°  F. 

Total  heat  at  26.8  pounds,  X^  =  1161.4  thermal  units. 

Heat  of  vaporization  at  84.6  pounds,  /•  =  896.8  thermal 
units. 

Heat  of  the  liquid  at  84.6  pounds,  y  =  286.2  thermal 
units. 

1161.4  +  0.4S  (268.2—243.9)  —286.2 
Priming  =  1 ^^ =  ^.002 

a  result  that  is  commonly  stated  as  ^^  per  cent  priming. 

Steam  dehvered  by  a  boiler  or  supplied  to  an  engine  com- 
monly contains  a  small  amount  of  moisture,  but  if  the  steam 
is  very  wet  from  any  cause  it  may  fail  to  superheat  in  the 
calorimeter  and  in  such  case  the  calorimeter  cannot  be  used 
for  determining  its  quaKty.  Should  this  occur  in  a  boiler 
test,  it  indicates  either  that  the  design  of  the  boiler  is  defect- 
ive or  that  it  is  in  bad  condition  and  needs  cleaning.  The 
steam  supplied  to  an  engine  may  be  deprived  of  the  greater 
part  of  its  moisture,  if  it  be  very  wet,  by  passing  it  through 
a  separator.  It  has  been  found  that  steam  used  in  good 
ordinary  practice  will  always  superheat  in  the  tlirottUng 
calorimeter. 

While  it  is  advisable  that  the  gages  and  thermometer 
used  with  the  throtthng  calorimeter  should  be  of  first  qual- 
ity and  entirely  reliable,  the  errors  that  such  instrmnents 
are  liable  to  have  do  not  have  a  serious  effect  on  the  result. 
Thus,  at  100  pounds  absolute  and  with  atmospheric  pres- 
sure in  the  calorimeter,  10°  F.  superheating  indicates  0.035 
priming ;  should  the  thermometer  be  wrong  5°  F.  and  in- 
dicate 15°  F.,  the  priming  will  appear  to  be  0.032.     In  a 


54  THE  THROTTLING  CALORIMETER 

similar  manner  it  will  be  found  that  an  error  of  a  pound  or 
two  in  the  pressure  of  the  steam  in  the  steam  pipe  will  have 
an  insignificant  eflPect  on  the  result  of  a  test.  The  effect  of 
an  error  in  the  reading  of  the  pressure  in  the  calorimeter  is 
somewhat  more  serious  and  care  should  be  taken  to  have 
that  gage  correct. 

A  glass  U  tube  filled  partially  full  of  mercury  is  sometimes 
used  to  give  the  pressure  in  the  calorimeter  instead  of  the 
gage  B. 

The  leg  of  tliis  colmnn  which  connects  with  the  calorim- 
eter will  after  a  short  time  have  some  water  collect  on  top 
of  the  mercury. 

Water  should  then  be  poured  into  the  other  or  open  leg 
of  the  column  so  as  to  keep  the  amount  in  each  leg  the 
same. 


/ 


CHAPTER  V 


HOW  TO  HANDLE  AND  TAKE  CARE  OF  A  CROSBY 
INDICATOR 

The  indicator  is  a  delicate  instrument,  and  in  order  to 
secure  good  results  from  its  use,  it  must  be  handled  with 
care  and  be  kept  in  good  order. 

The  Standard  Steam  Engine  Indicator 

To  remove  the  piston  and  spring,  unscrew  the  cap  ;  then 
take  hold  of  the  sleeve  and  lift  all  the  connected  parts  free 
from  the  cylinder.  This  gives  access  to  all  the  parts  to 
clean  and  oil  them. 

Never  remove  the  pins  or  screws  from  the  joints  of  the 
pencil  movement,  but  keep  them  well  oiled. 

Important.  In  the  under  side  of  the 
shoulder  of  the  piston-rod  B,  is  a  circular 
channel  formed  to  receive  the  upper  edge 
of  the  slotted  socket  of  the  piston  A.  In 
connecting  the  piston-rod  to  the  piston  in 
the  process  of  putting  in  a  spring,  first  start 
back  the  piston-screw  at  the  bottom  of  the 
piston,  insert  the  spring,  and  then  the  pis- 
ton-i'od,  and  BE  SURf2  to  screw  the  piston-rod  into  the 
socket  as  far  as  it  will  go  ;  that  is,  until  the  upper  end  of 
the  socket,  a^,  is  brought  firmly  against  the  bottom  of  the 
channel,  b^,  in  the  piston-rod.  This  insures  a  perfectly  cen- 
tral alignment  of  the  parts  and  therefore  a  perfectly  free 
movement  of  the  piston  within  the  cylinder.  Last,  screw 
up  the  piston-screw  lightly  against  the  btsad. 

To  attach  a  spring.  Hold  the  hollow  wrench  in  an  in- 
verted position  and  insert  the  piston-rod  until  its  hexagonal 
part  engages  the  wrench ;  then,  with  the  spring  inverted, 

55 


56  HOW  TO  HANDLE  A  CROSBY  INDICATOR 

insert  the  combined  wrench  and  piston-rod  until  the  bead  of 
the  spring  rests  in  the  concaved  end  of  the  latter ;  then  in- 
vert the  piston  and  jjass  the  transverse  wire  at  the  bottom 
of  the  sjjring  through  the  slot  until  the  threads  at  the  bot- 
tom of  the  piston-rod  engage  those  inside  the  socket  of  the 
piston,  and  with  the  wi'ench  screw  it  in  as  far  as  it  will  go  ; 
that  is,  until  the  upper  edge  of  the  socket  is  in  contact  with 
the  bottom  of  the  channel  in  the  shoulder  of  the  piston-rod. 
The  piston-screw  should  be  loosened  slightly  before  this  last 
operation  and  afterwards  set  up  against  the  bead  lightly,  to 
provide  against  any  lost  motion,  yet  not  so  as  to  make  it 
rigid.  Next,  hold  the  sleeve  and  cap  in  an  upright  posi- 
tion —  so  that  the  pencil  lever  will  drop  to  its  lowest  point 
—  and  engage  the  threads  of  the  swivel  head  with  those  in- 
side the  piston-rod  and  screw  it  up  until  the  threads  on  the 
lower  projection  of  the  cap  engage  those  in  the  spring  head, 
and  continue  the  process  until  the  latter  is  screwed  lirmly 
up  against  the  caj).  Then,  letting  the  cap  go  free  and  hold- 
ing only  by  the  sleeve,  continue  to  turn  the  piston  (together 
with  its  connections)  until  the  top  of  the  piston-rod  is  flush 
with  the  shoulder  on  the  swivel  head. 

The  piston  and  its  connections  may  now  be  inserted  in 
the  cylinder  and  the  cap  screwed  down,  which  will  carry 
all  parts  into  their  proper  places. 

To  detach  a  spring  sunply  reverse  this  process. 

To  change  the  location  of  the  atmospheric  line  of  the 
diagram.  First,  unscrew  the  cap  and  lift  the  sleeve,  with 
its  connections,  from  the  cylinder  ;  then  —  holding  the  sleeve 
with  the  left  hand  —  with  the  right  hand  turn  the  piston 
and  connected  parts  towards  the  left,  and  the  pencil  point 
will  be  raised,  or  to  the  right  and  it  will  be  lowered.  One 
complete  revolution  of  the  piston  will  raise  or  lower  the 
pencil  point  ^  inch  and  this  should  be  the  guide  for  what- 
ever amount  of  elevation  or  depression  of  the  atmospheric 
line  is  needed. 


HOW  TO  HAXDLE  A  CROSBY  INDICATOR  57 

To  change  to  a  left-haml  instrument.  If  it  is  desired  to 
nitike  tliis  change :  First,  remove  the  drum  shell  from  its 
base  by  a  straight  upward  pull ;  then,  with  the  hollow 
wTench,  remove  the  hexagonal  stop-screw  in  the  drmn  base, 
and  screw  it  into  the  vacant  hole  marked  L ;  next,  reverse 
the  position  of  the  adjusting  handle  in  the  arm ;  also,  the 
position  of  the  metallic  point  iii  the  pencil  lever ;  then 
replace  the  drum  and  the  change  from  right  to  left  will  be 
completed. 

This  applies  to  all  indicators  except  Standard  Indicators 
numbered  below  3737. 

The  tension  on  the  drum,  spring  may  be  increased  or 
diminished  according  to  the  speed  of  the  engine  on  which  the 
instrument  is  to  be  used,  as  foUows  :  Remove  the  drum 
shell  by  a  straight  upward  puU ;  then  raise  the  head  of  the 
spring  above  the  square  part  of  the  spindle  and  turn  it  to 
the  right  for  more  or  to  the  left  for  less  tension,  as  required  ; 
then  replace  the  head  on  the  spindle. 

Before  attaching  the  indicator  to  an  engine,  be  sure 
to  blow  steam  freely  through  the  pipes  and  cock  to  remove 
any  particles  of  dust  or  grit  that  may  have  lodged  in 
them. 

After  using  the  indicator  it  should  be  carefully  wiped  and 
oiled.  For  tliis  purpose  it  is  not  often  necessary  to  disturb 
the  paper  drmn,  but  the  cylinder  cap  should  be  unscrewed 
and  all  the  connected  parts  lifted  out ;  then  the  piston, 
piston-rod,  and  spring  should  be  detached  and  all  carefully 
wiped  with  cloth  or  tissue  paper  until  perfectly  dry,  then 
slightly  oiled  with  a  lubricant  of  good  quality  ;  the  inside  of 
the  cylinder  should  also  be  oiled.  After  this  is  done  the 
piston  and  ])iston-i'od  should  be  replaced  in  the  cylinder,  but 
the  spriiig  should  be  kept  on  its  stud  in  the  box  when  the 
instrument  is  not  in  use.  The  box  shoidd  be  kept  in  a  dry 
place. 

After  the  indicator  has  been  unused  for  any  length  of  time 


58  HOW  TO  HANDLE  A  CROSBY  IXDICATOR 

tlie  oil  used  at  its  last  cleaning  niay  have  become  gi'itty  or 
g^ummy ;  it  should  he  wiped  oil:  with  a  soft  cloth  or  tissue 
paper  saturated  with  naphtha  or  benzine,  and  then  freshly 
oiled  before  it  is  used.  This  keeps  the  instrument  in  prime 
condition  and  insures  the  best  results.  An  occasional 
naphtha  bath  will  cleanse  every  part ;  but  oil  should  be 
thoroughly  ajjplied  afterwards  to  prevent  corrosion. 

If  any  grit  or  other  obstruction  gets  into  the  cylinder  it 
may  score  the  cylinder  wall  and  also  cause  friction  and  stick- 
ing of  the  piston.  This  will  seriously  affect  the  diagram 
and  lead  to  bad  results.  It  is  not  difficult  to  detect  such 
trouble  and  it  should  be  remedied  at  once  by  taking  out 
the  piston,  detaching  the  paits  and  cleaning  them  as 
above  described,  Avhen  the  disturbing  cause  will  generally 
be  removed.  The  inner  wall  of  the  cylinder  should  l)e 
frequently  lubricated. 

It  is  essential  to  know  whether  or  not  the  indicator  is  in 
good  condition  for  vise  ;  especially,  to  know  that  the  piston 
has  perfect  freedom  of  motion  and  is  unobstructed  by  undue 
friction.  To  test  this  successfully,  detach  the  spring  and 
afterwards  replace  the  piston  and  piston-rod  in  their  usual 
position,  then,  holding  the  indicator  in  an  upright  position 
by  the  cylinder,  in  the  left  hand,  raise  the  pencil  arm  to  its 
highest  point  with  the  right  hand  and  let  it  drop.  It  should 
freely  descend  to  its  lowest  point.  If  the  opening  at  the 
bottom  of  the  indicator  cylinder  be  closed,  by  placing  the 
thumb  over  it,  the  jjiston  should  descend  slowly  from  its 
highest  point,  if  there  is  no  excessive  clearance  or  leakage 
past  the  piston.  These  tests  should  be  made  only  when  all 
the  parts  are  warm  from  the  steam,  in  the  condition  as 
actually  used,  and  the  piston  and  cylinder  should  be  care- 
fully wdped  and  lubricated  beforehand,  at  the  time  when  the 
sjiring  is  removed. 

The  pencil  should  always  have  a  smooth,  fine  ])<)int ;  a 
fine  file  is  the  best  instrument  to  use  to  sharpen  it. 


INDICATOR  SPRIXftS  69 

The  Crosby  New  Steam  Engine  Indicator 

To  remove  the  piston .  from  the  cylinder,  unscrew  the  cap 
and  lift  it  ^\'ith  the  plate  supporting  the  posts  and  spring 
from  the  indicator. 

The  attachment  of  the  sjirmg  is  easily  and  quickly  made. 
Remove  the  knurled  nut  above  the  l)ead  and  release  the 
binding  nut  below  the  spring  head  and  then  unscrew  the 
spring  from  the  threaded  busliing  of  the  cross-bar  to  wliich 
it  is  attached. 

When  the  spring  is  in  place,  the  pencil  may  be  adjusted 
to  any  desu'ed  position  on  the  drum  by  loosening  the  binding 
nut  below  the  spring  head  and  screwing  the  spring  upward 
or  downward,  carrying  with  it  the  pencil  mechanism.  So 
located,  with  the  binding  nut  again  screwed  firmly  into 
place  to  lock  the  spring,  the  pencil  is  held  in  position. 

The  suggestions  and  advice  as  to  the  care  of  the  Standard 
Steam  Engine  Indicator  apply  equally  weU  to  the  Crosby 
New  Indicator. 

INDICATOR  SPRINGS 

Indicator  springs  are  made  of  different  sizes  of  steel  wire, 
to  adapt  them,  in  point  of  strength,  to  different  pressures  of 
steam. 

To  adapt  the  indicator  to  any  steam  pressure,  springs  are 
made  to  the  following  scales  : 

4     8      12      16      20      30     40      50      60      80      100      120      150      180 

The  numl)or  stamped  on  the  spring  represents  the  number 
of  j)ounds  pressure  to  the  square  inch  which  are  reipiired  to 
compress  it  sufficiently  to  move  the  pencil  vertically  1  inch 
on  the  diagram.  The  strength  of  the  spring  that  should  be 
used  for  indicating  an  engine  depends  upon  the  maximum 
steam  pressure  to  which  it  will  be  subjected ;  it  should  be 
of  such  a  strength  or  number  that  the  diagram  will  not 
be    over    If    inches  liigh.     The  proper  spring    to  be  used 


00  INDICATOR  SCALES 

in  any  given  case  may  be  found  as  follows :  Divide 
the  boiler  pi'essure,  exjjressed  in  pounds,  by  the  desired 
height  of  the  diagram,  expressed  in  inclies,  and  the  result 
will  be  the  number  of  the  spring  required.  For  instance, 
if  the  boiler  jjressure  is  70  pounds  and  the  desired  height  of 
the  diagram  is  If  inches,  then  70  -I-  If  =  40,  the  number 
of  the  sjjring  required. 

In  practice,  the  best  diagram  for  measuring  and  inter- 
preting is  one  in  which  the  length  is  not  more  than  twice 
the  height,  for  the  reason  that  the  points  of  cut-off,  ex- 
haust and  compression  are  better  defined  than  in  a  longer 
diagram. 

The  late  John  C.  Hoadley,  an  eminent  authority  in  the 
use  of  the  steam  engine  indicator,  said  : 

"  There  are  good  reasons  for  keeping  the  diagram  of  very 
moderate  length.  From  2^  to  3  inches  will  be  found  long 
enough  to  admit  of  all  useful  division,  and  the  movement  of 
the  paper  cylinder  will  be  slower,  and  the  tracing  correspond- 
ingly more  delicate  than  if  a  longer  card  is  made.  A  similar 
remark  applies  equally  well  to  the  vertical  motion,  which  can 
be  reduced  to  any  amount  desired  by  using  springs  of  suit- 
able stiffness." 

Sir  Frederick  Bramwell  succeeded  in  obtaining  very  satis- 
factory diagrams  at  extraordinary  speeds  and  high  pres- 
sures, by  limiting  the  dimensions  to  one  inch  in  length  and 
width,  but  this  was  an  extreme  case.  It  is  generally  more 
convenient  and  satisfactory  to  make  the  length  about  2^  to 
3^  inches,  and  the  height  from  the  atmospheric  line  about 
1^  to  If  inches,  by  selecting  a  spring  adapted  to  the  pres- 
sure. 

INDICATOR  SCALES 

The  scales  for  measuring  diagrams  are  sometimes  made 
of  steel,  with  several  different  graduations  marked  on  each; 
they  are  more  often  made  of  boxwood,  and  these  we  recom- 


INDICATOR  SCALES  61 

mend  as  being  more  easily  read  and  less  liable  to  be  mis- 
ajjplied,  as  there  is  only  one  graduation  marked  on  each 
scale  of  tliis  kind.  The  scale  with  wliich  to  measure  the 
height  of  a  diagi-am  must  correspond  with  the  nTiniber  of 
the  spring  used  in  the  indicator  when  the  diagram  is  taken. 
For  a  diagi-ani  taken  with  a  number  40  spring,  use  a  scale 
ga-aduated  in  40  divisions  to  the  inch,  or  for  a  diagram  taken 
with  a  number  60  spring,  use  a  scale  graduated  in  60  divi- 
sions to  the  inch,  and  so  of  all  other  springs. 

Place  the  scale  on  the  diagi'am  at  right  angles  to  the 
atmospheric  line  with  the  zero  mark  of  the  scale  exactly  on 
that  line  ;  the  figures  set  against  these  di\asions  show  —  at 
whatever  point  the  line  of  the  diagram  crosses  the  edge  of 
the  scale  — ■  the  pressure  per  square  inch  exerted  by  the 
steam  on  the  piston  of  the  indicator  in  tracing  it.  The 
divisions  below  the  zero  point  show  vacmun. 

The  most  common  scales  are  those  numbered  40,  50,  and 
60  ;  that  is,  an  inch  of  vertical  height  on  the  scale  represents, 
according  to  the  number  of  the  corresponding  spring  used. 
40,  50,  or  60  pounds  of  steam  pressure  per  square  inch  in 
the  cylinder. 


CHAPTER   VT 
HOW  AND  WHERE  TO  ATTACH  THE  INDICATOR 

The  imlieator  should  he  attached  close  to  the  cylinder 
whenevei'  practicahle,  especially  on  high  speed  engines.  If 
pipes  must  be  used  they  should  not  be  smaller  than  half  an 
inch  in  diameter  and  as  short  and  direct  as  possible ;  if  long 
pipes  are  needed  they  should  be  slightly  larger  than  half  an 
inch  and  covered  with  a  non-conducting  material. 

Diagrams  should  be  taken  from  both  ends  of  the  cylinder 
of  an  engine.  If  the  diagram  from  one  end  is  satisfactory 
it  is  not  safe  to  assimie  that  one  taken  at  the  other  end  will 
be  equally  so  ;  it  is  often  otherwise,  owing  to  the  varying 
conditions  usually  found.  The  lengths  of  thoroughfares, 
the  points  of  valve  opening  and  closing,  and  the  lead,  are 
variable  and  should  be  carefully  adjusted  to  secure  the  best 
results,  and  this  can  only  be  done  through  the  instrmnen- 
taUty  of  an  indicator. 


When  only  one  indicator  is  employed,  it  is  generally 
attached  to  a  three-way  cock  (Fig.  12),  which  is  located 
midway  in  the  line  of  pipe  connecting  the  holes  at  either 
end  of  the  cylinder ;  by  this  arrangement  diagrams  can  be 
taken  from  either  end  simjjly  by  turning  the  handle  of  the 

62 


HOW  AXD  WHKRE  TO  ATTACH  TH?:  IXBICATOR  63 

thi-ee-way  cock.  In  such  a  case,  the  second  diagram  should 
he  taken  as  quickly  as  possihle  after  the  first,  so  as  to  he 
under  hke  conditions  of  speed,  pressiu'e,  and  load. 

The  indicator  can  he  used  in  a  horizontal  position,  hut 
it  is  more  convenient  to  take  diagrams  when  it  is  in  a  A'er- 
tical  position,  and  this  can  generally  he  ohtained,  when 
attaching-  to  a  vertical  engine,  hy  using  a  short  pii)e  with  a 
quarter  upward  hend.  No  putty  or  red  lead  should  he  used 
in  nuiking  any  joints,  as  particles  of  it  may  he  carried  hy 
the  steam  into  the  indicator,  and  great  harm  result  thei*e- 
from  ;  if  a  screw  fits  loosely,  mud  into  the  tlii'eads  a  little 
cotton  waste,  which  will  make  a  steam-tight  joint.  The 
indicator  should  never  he  set  so  as  to  communicate  Avith 
thorouglifares  where  a  current  of  steam  will  flow  past  the 
orifice  leading  to  the  indicator,  as  the  diagrams  taken  under 
such  conditions  would  he  of  no  practical  value. 

The  cyhnders  of  most  modern  steam  engines  are  drilled 
and  tapped  for  the  indicator  and  have  plugs  screwed  into 
the  holes,  which  can  readily  he  removed  and  the  proper 
indicator  connections  inserted.  But  when  this  is  not  the 
case,  the  engineer  should  he  competent  to  do  it  under  the 
directions  here  given. 

When  drilling  holes  in  the  cyhnder  the  heads  should  he 
removed  if  convenient,  so  that  one  may  know  the  exact 
position  of  the  piston,  the  size  of  ports  and  passages,  and  he 
ahle  to  remove  every  chip  or  particle  of  grit  which  might 
otherAAase  do  harm  in  the  cylinder  or  he  carried  into  the 
indicator  and  injure  it.  When  the  heads  cannot  be  taken 
off,  it  can  he  arranged  so  that  a  little  steam  may  he  let  into 
the  cylinder,  when  the  drill  has  nearly  penetrated  its  shell, 
so  that  the  cliips  may  he  hlown  outward  —  care  heing  taken 
not  to  scald  the  operator. 

Each  end  of  the  cyhnder  should  he  drilled  and  tapped 
for  ^-inch  pipe  thi^ead.  The  holes  must  always  he  drilled 
into  the  clearance  space,  at  points  beyond  the  range  of  the 


64  HOW  AJSJ)  WHERE  TO  ATTACH  THE  IXpICATOK 

piwton  when  at  the  end  of  the  stroke,  so  as  not  to  be  ob- 
structed by  it,  and  away  from  steam  passages,  to  avoid 
strong  currents  of  steam.  By  placing  the  engine  on  a  dead 
center,  it  is  easy  to  tell  how  much  clearance  there  is,  and 
the  hole  should  be  drilled  into  the  middle  of  this  s])ace  ;  the 
same  process  should  be  repeated  at  the  other  end  of  the 
cylinder. 

■  On  horizontal  engines  the  most  common  practice  is  to 
drill  and  tap  holes  in  the  side  of  the  cylinder  at  each  end 
and  insert  short  ^-inch  pipes  with  quarter  upward  bends, 
into  which  the  indicator  cocks  may  be  screwed  ;  on  some 
horizontal  engines  it  niay  be  more  convenient  to  drill  and 
tap  into  the  top  of  the  cylinder  at  each  end  and  screw  the 
cocks  directly  into  the  holes.  On  vertical  engines,  for  the 
upper  end  of  the  cylinder  the  cock  may  be  screwed  into 
the  upper  head  or  coiner,  and  for  the  lower  end,  into  the 
side  of  the  cylinder,  after  drilling  and  ta2)ping  the  necessary 
liole.  It  is  preferable  to  drill  the  holes  in  the  sides  of  a 
cylinder  rather  than  the  heads,  because  the  former  gives 
better  results  and  recpiires  less  pi})e  and  fittings. 

Before  deciding  just  where  to  drill  tlie  holes  it  is  wise  to 
(consider  (ill  the  conditions  of  the  case  and  devise  the  tr/mle 
plan  for  indicating  the  engine. 

Sometimes  a  driun  motion  can  be  erected  more  advan- 
tageously in  one  place  or  position  in  the  engine  room  than 
another,  or  one  kind  niay  be  better  adapted  for  a  given 
])lace  than  another.  Again,  the  ty2)e  of  engine  and  jjosition 
of  the  steam  chest,  the  kind  of  cross-head  and  the  best 
means  for  attaching  to  it,  the  position  of  the  eccentric,  its 
rods  and  connections,  all  should  be  taken  into  account  when 
determining  the  best  places  to  drill  the  cylinder  and  locate 
the  indicator,  in  order  to  secure  a  proper  connection  with 
the  reducing  motion,  a  j)erfectly  free  passage  for  steam 
to  the  indicator  and  the  most  convenient  access  to  the  in- 
strument for  taking  diagrams. 


CHAFI'KR   VII 


DRUM    MOTION 


Tlie  motion  of  tlu-  i)apt'r  diuiu  may  l)e  derived  from  any 
part  of  the  engine  which  has  a  movement  coincident  with 
tliat  of  the  piston.  In  general  practice  and  in  a  large 
majority  of  cases,  the  cross-head  is  chosen  as  being  the  most 
reliable  and  convenient. 

The  movement  of  the  cross-head,  whatevei"  it  actually  is, 
must,  ]>y  appropriate  mechanism,  be  reduced  to  the  length 
of  the  diagram  to  be  taken,  and  tliis 
reduced  motion  must  be,  in  point  of 
rapidity,  in  exact  ratio  to  the  motion 
of  the  piston. 

To  obtain  this  reduced  motion, 
various  devices  may  be  employed. 

The  reducing  lever  in  some  one 
of  its  various  forms  can  be  easily 
made  and  adapted  to  suit  almost 
any  conditions. 

A  common  form  of  this  device  is 
shown  in  Fig.  13,  and  answers  fairly 
well  for  lai'ge  and  quick  running- 
engines.  It  should  be  made  of 
straight  grained  pine,  one  inch  oi* 
more  in  thickness,  al)out  tlu'ee  inches 
wide  at  the  top.  and  tapering  to  a 
width  of    about   two   iiudies    at   the 

bottom;  its  length  sliould  be  at   least   one  and  a  half    times 
the  length  of  the  stroke  of  the  piston. 

Tlie  lever.  A,  is  suspended  by  a  bolt  from  the  ceiling  or 
from  a  truss  or  frame  overhead,  ju'epared  for  that  purpose. 


Fig.  13 


(55 


66  DRUM  MOTION 

in  such  a  manner  as  to  permit  it  to  swing  edgewise  and 
parallel  with  the  guides  of  the  engine.  Near  the  bottom  of 
the  lever  is  a  steel  stud,  secured  hy  a  nut  on  the  outside 
shown  at  B.  This  stud  has  a  T-head  projecting  inwardly 
from  the  lever,  and  is  formed  to  run  freely,  but  w^thout 
looseness,  in  a  T-slot,  cut  in  an  iron  plate,  and  firmly 
attached  to  the  center  of  the  cross-head,  which,  as  it  moves  to 
and  fro,  gives  to  the  lever  the  necessaiy  swinging  motion. 

Fig.  14  shows  the  arrangement  of  the  T-headed  stud,  or, 
in  connection  with  the  slotted  iron  plate,  c :  one  of  the 
screws  by  which  it  is  attached  to  the  cross-head  is  shown  at  d. 
The  head  of  the  stud  should  be  about  one  inch  in  diameter 
and  the  shank  about  one-half  inch.  The  T-slot  is  milled  out 
of  a  cast-iron  plate  of  suitable  size  and  shape  to  give  the 
proper  run  for  the  stud. 

When  the  lever  is  j)erpendicular,  or  in  the  middle  of  its 
path,  the  stud  should  be  near  the  bottom  of  the  slot,  wdiich 
should  be  long  enough  to  retain  the  stud  when  the  cross- 
head  is  at  the  exti-eme  end  of  the  stroke. 

By  this  de\ace  the  bottom  end  of  the  lever  is  moved  the 
full  distance  that  the  cross-head  travels  in  either  direction, 
and  for  this  reason  it  is  more  accurate  than  a  lever  of  the 
same  kind  having  its  lower  end  slotted  to  work  on  a  stud 
inserted  in  the  cross-head,  as  is  sometimes  used.  I)  is  a 
small  pulley  placed  near  and  on  a  level  with  the  pin  in  the 
lever,  for  the  indicator  cord  to  pass  over. 

While  this  form  of  reducing  lever  is  commonly  made  Avith 
a,  p'u^  for  attaching  the  indicator  cord,  greater  constancy  of 
motion  for  the  di'um  would  lie  attained  by  the  use  of  a 
sector,  such  as  is  shown  at  S  in  Hg.  15. 

To  find  the  point  on  the  lever  at  which  to  attach  the  in- 
dicator cord,  proceed  as  follows  :  Divide  the  length  of  the 
lever  by  the  length  of  the  piston  stroke,  and  multiply  the 
quotient  by  the  required  length  of  the  diagram,  all  exju'essed 
in  inches  and  decimals  of  an  inch,  and  the  product  will  be 


DRUM  MOTION 


6; 


the  ]iroper  distaiu-e  from  the  pivot  in  the  top  of  lever  to  the 
point  of  attac'luiient. 

For  example  :  If  the  lever  is  48  inches  long  and  the 
piston  stroke  is  30  inches,  and  we  wish  to  obtain  a  diagi-am 
3^  inches  long,  we  have  48  -^  30  =  1.6  ;  1.6  X  3.5"  =  5.6". 
tlie  radius  required  to  give  a  3.^  inch  diagram.  If  we  re- 
(piire  a  diagram  4^  inches  long,  then :  1.6  X  4.5"  =  7.2  , 
the  radius  required  to  give  a  44-  inch  diagram. 

The  object  of  all  mechanisms  for  actuating  the  drmn  of 
the  indicator  should  be  such  that  the  relation  of  piston  to 
drum  movement  will  be  constant.  Such  constancy  can- 
not, however,  be  fully  attained  by  the  use  of  any  form  of 
reducing  lever,  and  so  should  not  be  employed  when  im- 
portant adjustments  or  tests  are  to  be  made.  Their  simplic- 
ity and  the  small  expenditure  of  time  and  money  in  their 
construction  may  entitle  them  to  favorable  consideration 
on  the  part  of  beginners 
in  the  use  of  the  indicator, 
and  when  only  ordinary 
work  is  to  be  done. 

The  forms  shown  in 
Fig.  16,  Fig.  17,  Fig.  18, 
and  Fig.  19  are  correct  in 
principle,  and  when  care- 
fully constructed  may  be 
relied  upon  to  give  correct 
results. 

Tlif  Bruvihn  inilh'ii. 
shown  in  Fig.  15,  is  an- 
other form  of  reducing  "' 
lever,  and  one  often  used 
by  engineers,  especially  on 
locomotives.  It  can  lie 
quickly  and  cheaply  made  and  can  be  used  on  ahnost  any 
kind  of  engine.     The  swinging  lever  E  is  a  strip  of  straight 


Fig.  15 


68  DRUM  MOTION 

grained  pine,  one  inch  or  more  in  thickness,  three  to  four 
inches  wide,  and  from  one  and  a  half  to  two  times  as  long  as 
the  piston  stroke.  It  is  suspended  l)y  a  holt  or  screw,  serving 
as  a  pivot,  from  a  frame  or  truss  overhead  constructed  for 
that  pur])ose,  and  is  connected  at  its  lower  end  hy  the 
wooden  link  F,  to  the  usual  stud  or  ])in  fixed  in  the  center 
or  other  convenient  part  of  the  cross-head  ;  the  link  shoidd 
he  from  one-third  to  one-half  the  length  of  the  ])iston  stroke. 
In  the  illustration  the  proportions  of  lever  and  link  are  as 
(JO  to  15  ;  the  lever  being  two  times  and  the  link  one-half 
the  length  of  stroke. 

The  sector  S  may  he  constructed  of  wood  or  of  metal,  as 
here  shown  ;  it  has  a  groove  in  its  circmlar  edge  for  the 
cord  to  run  in  and  is  screwed  to  the  ujjper  end  of  the  lever 
or  pendulum,  so  that  its  center  will  coincide  with  the  center 
of  the  pivot  on  which  it  swings.  The  radius  of  the  sector 
which  is  necessary  to  give  the  jn'oper  motion  to  the  drum  to 
obtain  the  desired  length  of  iliagram  can  be  found  as  fol- 
lows :  Divide  the  length  of  the  lever  by  the  length  of  the 
piston  stroke  and  multiply  the  quotient  l)y  the  length  of 
diagram  desired,  and  the  product  will  be  the  required  radius, 
all  the  terms  being  expressed  in  inches  and  decimals  of  an 
inch.  F'or  example  :  If  the  lever  is  30  inches  long  and  the 
piston  stroke  is  20  inches,  and  we  wish  to  obtain  a  diagram 
3  inches  long,  we  have  30-^  20  =  1| ;  1|  X  3"  =  4^",  the 
radius  required  to  give  a  3  inch  diagram. 

When  the  (conditions  are  favorable,  the  lever  should  he 
hung  so  that  it  will  swing  in  a  vertical  plane,  parallel  with 
the  guides  and  in  line  with  the  indicator,  as  this  arrange- 
ment is  the  most  simple,  and  the  use  of  guide  pulleys  is 
avoided.  It  is  not  absolutely  necessary,  however,  that 
the  lever  shall  swing  in  a  vertical  jdane,  Imt  it  may  swing 
in  a  plane  at  any  angle  thereto,  where  the  conditions  re- 
quire it.  In  such  cases  a  man's  ingenuity  and  inventive 
faculty  must  aid  hun.      A  link  made  of  a  thin  strip  of 


DRUM  MOTION 


69 


steel,  that  will  twist  a  little,  is  in  some  cases  found  very 
convenient. 

Wlien  the  cross-head  is  at  midstroke  the  lever  must  hang 
plumb  and  the  pin  which  connects  its  lower  end  to  the  link 
nuist  be  as  much  helow  the  horizontal  line  of  motion  of  the 
atiid  in  the  cross-head  as  it  sweeps  (ihnve  that  line  at  either 
end  of  the  stroke.  See  the  dotted  line  for  an  illustration  of 
this  point,  which  is  important.  The  cord  must  lead  from 
tlie  sector  in  about  the  same  plane  with  its  swing. 

Carrying  pulleys  should  be  avoided  as  far  as  possible,  but 
whatever  number  is  necessary  should  be  firmly  placed.  The 
swinging  arm  of  the  gaiide-pulley  on  the  indicator  should 
always  be  fixed  in  the  direction  from  which  the  coi'd  is 
received. 

A  ])iece  of  piano  wire  is  often  used  to  replace  the  string 
leading'  from  tlie  sector  to  the  indicator. 


Fig.  16 


Tlie  pnntor/raph,  illustrated  in  Fig.  16,  is  another  style 
of  reducing  motion.  Although  theoretically  it  gives  a  per- 
fect motion,  owing  to  its  many  joints  it  niay  become  shaky 
and  give  erroneous  results,  unless  it  is  very  nicely  made  and 
carefully  used.     When  the  indicator  is  applied  to  the  side  of 


70 


DRUM  MOTION 


Fig.  17 


the  cylinder  the  pantograph  works  in  a  horizontal  plane. 
The  pivot  end  B  rests  on  a  post  or  other  support  set  oppo- 
site to  the  middle  of  the  guides,  and  the  working  end  A 
receives  motion  from  the  cross-head  —  to  which  it  is  attached 

hy  a  suitable  iron  with  a 
dr  hole  drilled  in  it  for  the 
stud  A  to  work  in.  By 
adjusting  the  support  for 
the  pivot  end  to  the 
proper  height  and  at  a 
proper  distance  from  the 
guides,  the  cord  may  he 
carried  directly  from  the 
pin  E  to  the  indicator 
without  the  need  of  car- 
rying pulleys.  The 
^(^ — ■  movable  bar  may  be  set 
forward  or  backward  by 
the  pins  C,  D,  so  as  to 
perfectly  adjust  the 
movement  of  the  pin  E 
to  the  required  length 
of  the  diagram  ;  this  pin 
niust  always  be  in  a 
straight  line  with  the 
stud  A  and  the  pivot  B. 
The  string  from  E 
should  always  lead  off  in 
a  line  parallel  to  the  pis- 
ton rod. 

The  directions  here 
given  for  constructing  and  arranging  drum  motions  are 
general  ;  special  cases  niay  require  modification  of  the 
forms  and  special  adaptation  of  the  means  here  described, 
all  of  which  call  forth  the  ingenuity  and  skill  of  the  engineer. 


OROSBY  REDUCING  WHEP:L  71 

Fig.  17  shows  a  pantograph  device  at  midstroke.  This  is 
made  of  bar  iron.  The  pins  d,  e,  f,  g,  are  nicely  fitted. 
The  indicator  cord  may  he  attached  at  b.  The  end  a  is  at- 
tached to  a  pin  on  the  cross-head.  The  fixed  fidcrum  is  at 
e.  a,  b,  and  c  must  always  lie  in  the  same  stmight  line, 
and  e  d,  b  n,  parallel  and  equal  to  f  g.  Also,  a  f:  nf  = 
stroke  of  piston  to  length  of  indicator  diagram. 

Fig.  18  illustrates  a  device  used  at  the  Massachusetts 
Institute  of  Technology.  /  is  a  rod  moving  in  a  slide  paral- 
lel to  the  piston-rod.  The  link  b  d  is  attached  to  /,  and  the 
link  a  e  to  the  cross-head,  a,  b,  and  c  must  always  lie  in 
the  same  straight  line,  a  e :  b  d  and  e  c  :  c  d,  =  stroke  of 
])iston  to  length  of  indicator  diagram.  The  cord  is  hooked 
on  a  i)in  at  g  :  it  is  well  to  have  a  pin  for  each  indicator 
used. 

Fig.  19  is  a  device  hy  Armand  St^vart  for  long  strokes. 
a  and  b  are  fixed  ends  of  cord  wrapped  around  a  pulley  D. 
The  indicator  cord  is  attached  to  a  small  pulley  d  and  passes 
around  a  guide  pulley  e.  D  and  d  are  attached  to  the 
cross-head.  Dia.  D  -^  dia.  d  =  stroke  of  the  piston  -^  hy  the 
difference  between  stroke  of  piston  and  length  of  card. 

The  redi(cing  wheel  is  another  device  for  giving  the 
proper  motion  to  the  paper  drum.  Although  old  in  prin- 
ciple, and  as  formerly  made  not  highly  approved  by  careful 
engineers,  it  is  now  coming  into  more  general  use,  and  the 
superior  manner  in  which  it  is  designed  and  constructed 
seems  to  warrant  this  change. 

CROSBY  REDUCING  WHEEL 

The  Crosby  reducing  wheel  is  attached  directly  to  the 
cylinder  cock  of  the  steam  engine,  and  has  connected  to  it 
the  steam  engine  indicator  which  it  is  to  serve  ;  thus  it 
forms  a  base  or  support  for  the  latter,  and  receives  all 
the  strains  and  shocks  in  the  operations  of  the  engine, 
to  the  relief  of  the  indicator.     All  its  parts  are  designed 


72 


CROSBY  REDUCING  WHEEL 


and  constructed  fov  strength,  accuracy,  and  durability. 
Its  bearings  are  not  only  nicely  adjiisted,  but  are  made 
comparatively  fi-ictionless  by  the  introduction  of  balls  run- 
ning in  liardened  tool  steel  bearings,  affording  lightness  and 
freedom  of  movement.  It  has  a  helical  spring  v^^hich  is 
more  active  in  recoil  than  the  volute  spring  in  common  use, 
this  being  a  very  essential  feature  for  accurate  results  on 
high  speed  engines.  The  cord  pulley  is  horizontal  to  allow 
the  cord  leading  to  the  engine  cross-head  to  take  any  direc- 
tion the  circumstances  may  require  without  regard  to  the 
position  of  the  indicator. 

Patented 


This  Citt  Shows  the  Crosby  Standard  Steam  Engine  Indicator 
Mounted  upon  the  Crosby  Reducing  Wheel 


CKOSBY  REDUCING  WHEEL  WITH  DETENT  •         73 

Special  tools  have  been  provided  for  making  it,  so  that 
like  parts  are  interchangeable,  and  when  worn  or  destroyed 
others  can  be  easily  siibstitnted  ;  in  other  words,  everything 
has  been  done  so  far  as  possible  to  make  the  instrument  in 
all  respects  as  excellent  for  its  purpose  as  is  the  Crosby 
indicator. 

It  is  adapted  to  receive  any  steam  engine  indicator  or  indi- 
cator cock  by  means  of  interchangeable  bushings ;  and  by  a 
series  of  sjieed  pulleys  it  can  he  adapted  to  all  steam  engines 
having  strokes  between  the  limits  of  14  inches  and  72  inches. 

Whenever  the  reducing  wheel  is  to  be  attached  to  a  ver- 
tical engine  an  elbow  nipple  is  provided,  which  will  allow 
the  cord  pulley  to  travel  in  the  proper  plane  for  guiding  it 
to  the  cross-head  of  the  engine,  with  the  indicator  in  an 
upright  position  as  usual. 

CROSBY  REDUCING  WHEEL  WITH  DETENT 

Patented 

The  detent  applied  to  the  Crosby  Reducing  Wheel  does 
not  affect  the  connection  between  it  and  the  engine,  and 
does  not  allow  the  cord  leading  from  the  indicator  drum  to 
the  reducing  wheel  to  slacken. 

When  the  clutch  is  thrown  in  to  stop  the  motion,  the  in- 
dicator drum  is  revolved  to  the  end  of  the  stroke  and  held 
there  by  the  drum  cord,  while  the  mechanism  of  the  detent 
controls  the  cord  leading  from  the  reducing  wheel  to  the 
cross-head  of  the  engine. 

When  the  clutch  is  i-eleased  and  the  motion  of  the  engine 
is  again  communicated  to  the  drum,  the  latter  takes  up  the 
motion  without  shock  from  the  point  where  it  stopped,  be- 
cause it  starts  from  a  state  of  rest  at  the  end  of  the  stroke. 
This  is  imj)ortant,  for  if  a  drum  is  stopped  and  held  by  a 
detent  in  midstroke  where  the  piston  is  running  at  its  high- 
est speed,  at  the  release  of  the  detent  the  drum  will  neces- 
sarily  start    again    at    such    liighest    speed    with    a    shock. 


74 


CROSBY  KEDUCIXG  WHEEL  WITH  DETENT 


This  Cut  Shows  the  Crosby  New  Indicator  Mounted  upon 
THE  Crosby  Reducing  Wheel  with  Detent 

Moreover,  as   such   a  detent   must    engage    at   the    highest 
speed,  it  often  fails  to  operate  and  always  wears  rapidly. 
Directions  for  using  the  Crosby  Reducing  Wheel,  either 
without  or  with  detent,  are  sent  w^ith  each  instrument. 


CROSBY  REDUCING  WHEEL  WITH  RECORDING   COUNTER 

Patented 

To  determine  the  number  of  revolutions  of  the  engine  per 
minute  an  ingenious  and  convenient  device  is  shown  by  the 
cut,  representing  the  Crosby  Reducing  Wheel  having  at- 
tached to  it  the  Crosby  Recording  Indicator  Counter. 


CROSBY  REDUCING  WHEKL  WITH  COUNTER 


75 


The  latter  is  actuated  by  the  moving  parts  of  the  reduc- 
ing wheel  and  records  on  a  chart  every  revolution  of  the 
engine  ;  so  that  during  the  taking  of  the  diagrams  by  the 
indicator  attached  to  the  reducing  wheel  the  revolutions  of 
the  engine  are  recorded  simultaneously. 


Its  capacity  to  record  5,000  revolutions  permits  its  use 
during  a  considerable  period  of  indicating  work  ;  and  the 
average  number  2)er  minute  so  determined  is  more  accurate 
for  such  purpose  than  if  the  revolutions  were  merely  counted 
intermittently  l)y  the  ordinary  speed  insti-uments.  Besides, 
tliere  is  thus  preserved  by  the  chart  a  record  of  the  work 
done,  to  be  filed  with  the  diagrams  taken  by  the  indicator 
for  future  consideration. 

It  has  recorded  upwards  of  4,000  revolutions  per  minute 
without  a  fault.  No  difficulty  will  arise  in  its  attaclmient 
and  use. 

After     the    reducing   wheel    has    been    adjusted    to    the 


76  IMPORTANT  SUGGESTIONS 

stroke  of  the  engine,  the  counter  is  attached  according  to 
the  following  dii-ections  : 

Loosen  the  clamping  nut  on  the  back  of  the  counter  ;  raise 
the  lever  to  its  vertical  position,  and  if  the  operating  pin 
does  not  drop,  press  it  lightly  downward.  Loosen  the  hexa- 
gon nut  below  the  guide  bracket  of  the  reducing  wheel  and 
slip  the  fork  of  the  counter  bracket  under  the  nut ;  adjust 
the  height  of  the  counter  on  its  bracket  so  that  the  opera- 
ting pin  of  the  counter  when  down  will  just  clear  the  guide 
bracket ;  tighten  all  the  nuts  securely.  To  start  the  coun- 
ter, thi'ow  the  finger  lever  down  ;  to  stop  it,  raise  the  lever 
to  its  vertical  position. 

Set  the  chart  at  zero.  Note  the  time  of  starting  and 
stopping  on  the  face  of  the  chart,  where  indicated. 

IMPORTANT  SUGGESTIONS 

In  all  cases  the  indicator  coixl  should  be  of  the  right 
length  to  prevent  the  paper  drum  from  recoiling  against  its 
stop ;  and  before  attaching  it  to  the  cross-head  of  the  en- 
gine it  should  be  drawn  out  its  full  length  to  ascertain 
whether  or  not  the  cords  on  the  indicator  and  reducing 
wheel  have  been  properly  adjusted. 

All  the  woi'king  parts  must  be  kept  well  oiled. 

The  reducing  wheel  is  adapted  to  be  used  with  a  steam 
engine  indicator  having  either  a  1|-  inch  or  2  inch  drum. 
As  indicators  Avith  2  inch  drums  are  now  more  commonly 
used,  the  reducing  wheel  is  ordinarily  provided  only  with 
stroke  pulleys  for  such  size  drum.  If  the  reducing  wheel  is 
to  be  used  with  an  indicator  having  the  1^  inch  drum,  it 
should  be  so  stated  in  order  to  receive  the  stroke  pulleys  of 
the  projjer  size. 

These  stroke  pulleys  are  provided  in  sets  and  can  be  so 
obtained.  With  the  2  inch  drum,  the  pro])er  stroke  pulleys 
will  give  cards  4  inches  long,  and  with  the  1^  inch  drum 
the  stroke  pulleys  are  calculated  to  give  cards  3  inches  long. 


TESTIXG  REDUCING  MECHANISM  77 

Busliings  may  be  obtained  for  attaching  other  than  the 
Cro.s])y  indicators,  and  elljow  nipples  are  made  for  attach- 
ing the  reducing  wheel  to  a  vertical  engine. 

TESTING  THE  ACCURACY  OF  REDUCING  MECHANISM 

Whatever  drum  motion  mechanism  is  used,  its  accuracy 
can  be  easily  tested  in  the  following  manner :  Lay  off  on 
the  engine  guides  points  at  ^,  ^,  and  f  of  the  stroke. 
Connect  the  indicator  with  the  drum  motion  in  the  same 
manner  as  for  taking  diagi'ams.  When  the  cross-head  is  on 
either  dead  center,  touch  the  pencil  to  the  paper  and  make 
a  vertical  mark,  and  in  the  same  way  make  vertical  marks 
when  the  cross-head  reaches  each  successive  quarter  point 
on  the  guides.  If  the  marks  are  exactly  at  fourths  on  the 
card,  the  motion  of  the  cross-head  has  been  accurately 
reduced. 


CHAPTER  VIII 
HOW  TO  TAKE  DIAGRAMS 

First  connect  the  indicator  to  the  indicator  cock. 

Adjust  the  guide  wheel  under  the  drum  so  that  the  cord 
leads  from  this  wheel  in  the  right  plane- 
All  reducing  motions  of  the  pantograph  type,  such  as  the 
lazy  tongs  shown  by  Fig.  16  and  the  modifications  shown 
hy  Figs.  17  and  18,  require  for  correct  reduction  of  motion 
that  the  string  to  the  indicator  should  run  in  a  line  parallel 
to  the  line  of  motion  of  the  piston-rod. 

AVith  reducing  motions  of  the  Brumbo  pulley  type,  shown 
by  Fig.  15,  it  makes  no  difference  at  what  angle  the  string 
leads  from  the  guide  wheel  to  the  sector.  The  string  must, 
of  course,  be  in  the  plane  of  the  sector. 

After  the  guide  wheels  under  the  drum  have  been  ad- 
justed and  fastened,  change  the  lo(;ation  of  the  hook  on 
the  drum  string  so  that  when  the  hook  is  pulled  away  out  as 
far  as  it  will  go,  it  overlaps  the  pin  or  ring  or  loop  or  what- 
ever is  provided  for  a  connection  on  the  reducing  motion, 
by  about  §■  of  an  inch.  Then  let  the  drum  spi-ing  pull  the 
hook  away  ])ack  and  note  how  near  the  hook  comes  to  the 
pin  or  loop  on  the  reducing  motion.  If  the  hook  is  drawn 
Ijack  ^  of  an  inch  beyond  the  travel  of  the  pin  or 
loop  on  the  reducing  motion  the  cord  is  the  right  length. 
Should  the  distance  at  this  end  be  1  inch,  and  at  the  other 
f  of  an  inch,  tlie  cord  should  l>e  lengthened  so  as  to  make 
the  distances  alike  at  the  two  extremes  of  the  travel. 

The  paper  is  now  put  on  the  drum.  The  paper  must  be 
tight  and  pushed  down  to  the  bottom  of  the  clips. 

There  are  two  ways  in  which  the  jjaper  may  be  held  by 
the  clips.      The  ends  of  the  paper  may  be  brought  out  in 

78 


HOW  TO  TAKE  DIAGRAJMS  79 

the  center  between  the  two  clips,  or  the  two  clips  may  he 
used  as  one  piece  and  the  two  ends  laj)ped  under  them. 

Next,  connect  the  drum  to  the  reducing  motion.  If  one 
understands  how  to  do  this,  it  makes  no  difference  whether 
the  engine  is  making  10  or  600  revolutions  per  minute. 
Oftentimes  it  is  amusing  to  watch  one  who  does  not  know 
how,  try  to  catch  the  loop  in  the  string  from  a  Brumho 
pulley  reducing  motion  on  a  high  speed  engine. 

With  one  hand  pull  the  hook  on  the  indicator  cord  out 
as  far  as  it  Avill  go.  With  the  other  hand  take  hold  of  the 
sti'ing  from  the  Brumlio  pulley  and  let  the  string  he  pulled 
through  your  fingers  till  the  loop  is  reached.  Hold  the  loop 
so  that  each  time  the  engine  reaches  the  crank  end  of  its 
stroke  you  will  feel  a  slight  pull  on  the  loop  due  to  the 
winding  of  the  string  on  the  sector.  The  hook  on  the  indi- 
cator cord  will  reach  |-  of  an  inch  heyond  the  end  of  the 
loop,  making  it  easy  to  connect.  The  speed  of  the  engine, 
it  will  be  seen,  does  not  make  any  difficulty  about  connect- 
ing on  if  this  method  is  used. 

Steam  is  now  turned  on  the  indicator  tlu'ough  the  indi- 
cator cock,  and  after  a  period  of  ten  seconds,  in  which  time 
the  indicator  is  being  heated  up  by  the  steam,  a  card  may 
be  taken  by  pressing  the  wooden  handle  moving  the  pencil 
mechanism  up  against  its  stop.  After  taking  the  card, 
close  the  cock  and  draw  an  atmospheric  line.  Then  discon- 
nect the  drum  string  from  the  reducing  motion. 

Should  the  lines  on  the  card  be  too  faint,  the  wooden 
handle  may  be  screwed  back  a  turn  or  two. 

Formerly,  graphite  was  used  for  the  marking  point  and 
ordinary  paper  as  drum  paper.  To-day  metallic  paper  (a 
paper  coated  Avith  a  salt  of  lead)  is  almost  universally  used 
and  the  marking  point  is  a  piece  of  soft  brass.  This  makes 
it  possible  to  get  very  fine  lines  on  the  card  and  to  take 
cards  with  very  little  pressure  on  the  marking  point.  Any 
friction  between  the  pencil  and  the  paper  makes  an  error  in 


80  HOW  TO  TAKE  DIA(;RAMS 

the  card,  and  cards  should  be  taken  with  as  faint  hnes  as 
possible  on  this  account. 

Make  notes  on  the  card  of  as  many  of  the  following  facts 
as  possible.  The  day  and  hour  of  taking  the  diagram  ; 
the  kind  of  engine  from  which  the  diagram  is  taken,  and 
which  eiigine,  if  one  of  a  pair ;  which  end  of  the  cylinder, 
the  diameter  of  the  cyhnder,  the  length  of  the  stroke,  the 
diameter  of  the  piston-rod,  and  the  number  of  revolutions 
per  minute  ;  the  position  of  the  throttle  ;  the  atmospheric 
pressure  ;  the  steam  pressure  at  the  boiler  and  at  the  engine, 
by  the  gages  ;  the  vacuum  by  the  gage  on  the  condenser  and 
the  temperature  of  the  feed  at  the  boiler  ;  if  the  engine  is 
compound,  the  pressure  in  the  receiver ;  the  scale  of  the 
spring  used  in  the  indicator  ;  the  volume  of  the  clearance  at 
each  end  of  the  cylinder,  and  what  per  cent  of  the  piston 
displacement  each  of  these  volumes  is.  (Directions  for 
ascertaining  the  volume  of  the  clearance,  and  what  per  cent 
that  volume  is  of  the  piston  displacement,  are  given  on 
pages  94  and  96.) 

It  is  often  useful  to  make  notes  of  special  circumstances 
of  importance,  such  as  a  description  of  the  boiler,  the  diame- 
ter and  length  of  the  steam  and  exhaust  pipes,  the  tempei'a- 
ture  of  the  feed  water,  the  quantity  of  water  consumed  per 
hour,  etc. 

On  a  locomotive,  note  the  tmie  of  passage  between  mile- 
posts  in  minutes  and  seconds,  from  which,  when  the  diame- 
ter of  the  drivers  is  known,  the  number  of  revolutions  per 
minute  may  be  calculated.  Note  also  the  position  of  the 
throttle  and  the  link,  the  size  of  the  blast  orifice,  the  weight 
of  the  train,  and  the  gradient. 

On  diagrams  from  marine  engines  note,  in  addition  to 
the  general  facts,  the  speed  of  the  ship  in  knots  per  hour, 
the  direction  and  force  of  the  wind,  the  direction  and  state 
of  the  sea,  the  diameter  and  pitch  of  the  sia-ew,  the  kind  of 
coal,  the  amount  consumed,  and  the  ashes  made  per  hour. 


chaptp:r  IX 

HOW  TO  FIND  THE  POWER  OF  AN  ENGINE 

To  find  the  power  actually  exerted  witliin  the  cylinder  of 
a  steam  engine,  it  is  necessary  to  ascertain  separately  three 
factors  and  the  product  o£  their  continued  multiplication. 
These  factors  are :  The  area  of  the  two  sides  of  the  ])iston ; 
the  total  travel  of  the  piston  in  feet  per  minute  ;  and  the 
mean  effective  pressure  urging  the  piston  forward,  desig- 
nated M.  E.  P. 

The  2)'iston  area.  This,  at  the  back  end,  is  the  same  as 
the  area  of  cross-section  of  the  cyHnder  ;  at  the  crank  end 
it  is  the  same,  less  the  area  of  cross-section  of  the  piston- 
rod.  These  areas  may  be  found  from  their  diameters  in  a 
ta]>le  of  the  areas  of  circles,  or  may  be  computed  by  multiply- 
ing the  square  of  the  diameter  in  inches  by  the  approximate 
nmnber  0.7854. 

The  trarel  of  the  jji-'^ton.  The  total  travel  of  the  piston 
in  feet  per  minute  is  found  by  nudtiplying  twice  the  length  of 
the  stroke  measured  in  feet,  by  the  number  of  revolutions  of 
the  crank  shaft  per  minute,  which  should  be  carefully  ascer- 
tained by  taking  the  mean  of  many  countings,  or  the  readings 
of  a  speed  counter  during  a  considerable  time.  The  mean 
piston  speed  will  be  expressed  in  terms  of  feet  per  minute. 

The  mean  effective  pressure.  There  are  several  approxi- 
mate methods  for  computing  the  mean  effective  pressure, 
on©  of  which  is  to  divide  the  diagram  into  ten  equal  parts, 
as  shown  in  Fig.  20.  Then  through  the  points  of  division 
draw  lines,  which  are  called  ordinates,  at  right  angles  to  the 
atmospheric  line.  The  mean  heights  or  pressures  of  the 
small  areas  thus  formed  are  indicated  by  the  dotted  lines 
midway  between  the  ordinates. 

81 


82 


MEASURING  THE  DIAGRAM 


The  mean  effective  pressure  of  the  whole  (of  each)  dia- 
gram may  now  he  found,  hy  measuring  (on  the  dotted  lines) 
the  mean  pressure  in  each  of  the  small  areas  with  the  scale 
corresponding  to  the  spring  used  in  taking  the  diagram. 


H    cd    2; 
K    h(    (-) 

O  w 


W   bs 


The  sum  of  these  mean  pressures,  divided  by  10,  the 
number  of  divisions,  will  give  the  mean  effective  pressure 
sought,  in  pounds  per  square  inch. 

If  a  diagram  has  many  irregularities  of  outline,  it  may  he 
necessary  to  divide  it  into  twenty  equal  divisions  to  insux'e  a 
correct   measurement  of  the  pressures ;  in  such  a  case  we 


MEASURING  THE  DIAGRAM 


83 


divide  the  sum  of  the  pressures  by  20  instead  of  10.  In 
other  cases,  when  irregularities  occur  only  in  a  part  of  a 
diagram,  it  is  only  necessary  to  subdivide  one  or  more  of 
the  ten  divisions  to  insure  greater  accuracy  in  that  part ;  in 
such  a  case  we  must  measure  the  pressure  in  each  subdivision 
and  divide  their  sum  by  2  to  get  the  mean  pressure  of  that 
division.  (See  Fig.  22  for  a  full  illustration  of  this  method.) 
If  the  scale  is  not  at  hand,  the  heights  of  the  divisions 
may  be  pricked  or  marked  ofE  on  a  strip  of  paper,  one  after 
the  other  continuously  until  all  are  measured ;  then  the 
distance  from  the  end  of  the  strip  to  the  last  mark  vnll 
represent  the  sum  of  all  the  measurements,  which  can  be 
measured  in  inches  with  an  ordinary  rule.  This  quantity, 
divided  by  the  number  of  divisions  in  the  diagram  —  or 
diagrams,  if  there  are  two  —  and  multiplied  by  the  scale  of 
the  spring  used,  will  give  the  average  or  mean  effective 
pressure,  the  same  as  by  the  other  method. 


Fig.  21 

When  there  is  a  loop  in  the  diagram,  as  in  Fig.  21,  the 
area  enclosed  in  the  loop  should  be  subtracted  from  the  other 
part,  as  it  represents  loss  of  efficiency. 

The  quickest  and  most  accurate  method  for  measuring  the 
diagram  and  finding  the  mean  effective  pressure  is  by  the 
use  of  Amsler's  Polar  Planimeter.  With  careful  manipula- 
tion, the  planimeter  will  give  the  exact  area  of  a  diagram  in 


84  MEASURIN(:t  THE  DIAGRAM 

square  inches  and  decimal  parts  thereof,  to  hundredths  of  a 
S(^uare  inch,  and  the  tedious  process  of  dividing  the  diagram 
into  equal  parts  and  measuring  their  average  pressures  or 
heights,  with  the  liability  of  making  ei'roi's,  is  avoided. 

Measure  the  diagram  with  the  planimeter  as  directed  in 
Chapter  IV,  at  page  45.  Divide  the  number  of  square 
inches  area  thus  found  by  the  length  A  of  the  diagram, 
expressed  in  inches  and  decimals,  and  the  result  will  be  the 
average  height  of  the  diagram.  Multiply  this  average 
height  by  the  scale  corresponding  to  tlie  spring  used  in 
taking  the  diagram  and  the  result  will  be  the  mean  effective 
pressure.  It  is  better  to  multiply  first  and  divide  afterwards 
to  avoid  troublesome  fractions. 

Fig.  22  illustrates  two  diagrams  divided  first  into  ten 
equal  spaces  and  then  each  end  space  subdivided  so  as  to 
more  accurately  measure  those  parts  of  each  in  which  the 
greatest  iriegularities  occur.  Observe  that  the  pressures  or 
heights  of  the  subdivisions  of  each  end  space  are  measured, 
and  the  sum  of  these  measurements  divided  by  2  to  get 
the  mean  pressure  or  height  of  that  one  of  the  ten  spaces. 

The  pressures  of  Diagram  No.  1,  as  measured  by  the 
scale,  are  set  in  a  column  on  the  left,  while  those  of  No.  2 
are  set  in  a  column  on  the  right.  The  sum  of  each  column 
divided  by  10  gives  the  M.  E.  P.  of  that  diagram. 

The  heights  of  Diagram  No.  1,  marked  off  on  a  slip  of 
paper  continuously,  measure  11.91  inches,  while  those  of 
No.  2  measure  11.95  inches  ;  these  quantities,  divided  by 
10  and  multiplied  by  50,  give  the  M.  E.  P.  of  each  diagram 
respectively,  and  if  accurately  measured,  will  be  the  same 
as  found  by  the  scale. 

These  diagrams,  when  measured  by  the  planuneter,  give 
results  which  are  substantially  the  same.  As  the  error 
of  the  planimeter  is  less  than  its  smallest  scale  graduation, 
this  method  of  finding  the  mean  effective  pressure  is  the 
most  accurate  as  well  as  the  most  convenient. 


measuring  the  diagram 
Fig.  22 


85 


Diagram  No.  1 
Pressurea 


Diagram  No.  2 
Pressurea 


10)  595.5 

M.E.  P.,  59.55  M.  E.  P.,   59.75 

Heights  of  Divisions  Measured  on  a  Strip  of  Paper 


Diagram  No.  1 

Diagram  No.  2 

10)  11.91  111. 

Divide  by  10 

10)  11.95  in. 

1.191 

1.195 

,50 

Multiply  by  proper  scale 

M. 

50 

M.E.  P.,   59.r.r.0 

E.  P.,   59.750 

Diagram  No.  1 
Square  inches,    4.43 
Length,  3.72 

Average  height,  1.191 
M.  E.  P.,  59.55  lbs 


Planimeter  Measurements 

Diagram  No.  2 
Square  inches,        4.46 
Length,  3.73 

Average  height,     1.195 
M.E.  P.,  59.75    lbs. 


86  CALCULATING  HORSE-POWER 

CALCULATING    \.  H.  P. 

Let  a  =  the  area  of  the  head  end  of  the  piston  in  square 
inches. 

Let  r  =  the  area  of  the  piston-rod  in  square  inches. 
Let  s  =  the  stroke  of  the  engine  in  feet. 
Let  n  =  the  number  of  revolutions  per  minute. 
The  I.  H.  P.,  or  indicated  horsepower,  of  the  liead  end  of 
the  cyhnder,  is 

a  X  (M.  E.  P.  of  head  end)  X  s  X  n 
33,000 

The  I.  H.  P.  of  the  crank  end  is 

(a  —  r)X  (M.  E.  P.  of  crank  end)  Xs  Xn 
33,000 

The  I.  H.  P.  of  the  cyhnder  is  the  sum  of  these  two. 

If  the  M.  E.  P.  and  the  revolutions  per  minute  are  each 

made   equal   to    1    in   the   preceding   expressions,   then  the 

result  obtained  from  each  is  the  I.  H.  P.  per  pound  M.  E.  P. 

at  one  revolution  per  minute.     These  factors  are  called  the 

engine  constants.     The  engine  constants  for  the  two  ends 

are  respectively 

a  X  s         _     (a  —  ?')  X  s 

and 

33,000  33,000 

If  the  valves  of  an  engine  are  well  adjusted  and  the 
M.  E.  P.  for  the  two  ends  of  the  cylinder  is  nearly  the 
same,  an  approximate  calculation  of  the  indicated  horse- 
power of  the  cylinder  may  be  made  by  multiplying  the 
average  M.  E.  P.  of  the  two  ends  by  the  number  of  revo- 
lutions per  minute  and  by  the  sum  of  the  engine  constants. 

DISCUSSION    OF    M.E.P. 

The  indicator  card  from  one  end  of  a  cylinder  shows  the 
pressures  on  tliat  end  during  a  revolution,  or  a  stroke 
foi'ward  and  a  stroke  back. 


CALCULATING  HORSE-POWER 


87 


The  Mean  Effective  Pressure,  M.  E.  P.  (improperly 
named  perhaps)  used  in  figuring  horsepower  is  calculated 
from  the  indicator  cards  as  already  explained. 

The  effective  pushing  pressure  or  pulling  pressure  per 
square  inch  of  piston  area  at  any  point  of  the  stroke  is  evi- 
dently the  difference  hetween  the  total  pressures  on  the  two 
sides  of  the  piston  at  that  point  divided  hy  the  piston  area. 
Obviously  the  average  pressure,  calculated  in  this  way,  would 
not  be  the  same  as  the  mean  effective  pressure. 

(See  discussion  of  stroke  cards  given  later  on.) 

That  the  horsepower  obtained  is  correct  when  the 
M.  E.  P.  is  calculated  as  previously  explained  is  shown  liy 
the  illustration  which  follows. 

Let  the  mean  pressure  above  the  atmospheric  line  corre- 
sponding to  line  a  b  c  d  ^  Pj-. 


A 

B 

Let  the  mean  pressiire  above  atmospheric  line  correspon<l- 
ing  to  line /' g  h  h=  Pj. 

Let  the  mean  pressure  above  the  atmospheric  line  corre- 
sponding to  h  i  f  =  Ef^. 


88  CALCULATING  HORSE-POWER 

■  Let  the  mean  pressure  above  the  atmospheric  line  corre- 
sponding to  d  e  a  =  Ef. 

Let  A  =  area  of  head  end  of  piston  in  square  inches. 

Let  B  =  area  of  crank  end  of  piston  in  square  inches. 

Let  s  =  stroke  in  feet. 

The  total  mean  pressure  on  the  piston-rod  during  the 
forward  stroke  of  the  piston  is 

A   Pf—B  E^ 

The  total  mean  pull  on  the  piston-rod  during  the  return 
stroke  is 

B  Ph  —  A  Ej- 

The  total  foot-pounds  per  revolution  is 

A  s  Pf—  B  s  74  +  B  s  P,  —  A  s  Ej. 

ovA  (Pf-E^)  s  +  B  {P,-E,)s 

Pf — Ef  is  the  mean  effective  pressure  of  the  forward 
card. 

P^  —  E^  is  the  mean  effective  pressure  of  the  crank  card. 

CALCULATING  HORSE-POWER  FROM  GAS   ENGINE  CARDS 

There  are  two  types  of  gas  engines  —  the  f oui-cycle  and 
the  two-cycle.  A  four-cycle  single  acting  engine  can  have 
but  one  working  stroke  in  four  strokes  or  in  two  revolu- 
tions. A  two-cycle  single  acting  engine  has  one  working 
stroke  per  revolution. 

There  are  two  classes  of  engines  of  the  four-cycle  tyjje. 
In  one  class  the  governing  is  by  missing  working  strokes 
when  the  engine  is  at  sjjeed.  The  proportion  of  missing 
strokes  to  working  strokes  varies  with  the  load.  At  full 
load  there  is  one  missing  stroke  to  seven  or  eight  firing 
strokes. 

In  the  other  class  there  is  a  working  stroke  regularly  at 
every  fourth  stroke,  but  the  power  of  the  working  stroke  is 
varied  By  throtthng    the  charge  as  it    is    drawn    into    the 


GAS  EXGL^E  HORSE-POWER  89 

cylinder  and  by  this  means  decreasing  the  pressure  at  the 
end  of  the  compression  stroke.  As  the  maximum  pressure 
at  explosion  increases  within  certain  limits  proportionately 
mth  the  pressure  at  the  end  of  compression,  it  follows  that 
the  greater  the  compression  the  greater  the  mean  effective 
pressure.  The  weight  of  the  charge  drawn  into  the  cylinder 
is  different  with  different  amounts  of  throttling. 

A  gas  engine  governing  liy  omitting  working  strokes,  on 
the  '"  hit  and  miss "  method,  may  have  its  firing  cycle  as 
follows  : 

Light  load  —  fire  1,  miss  5  ;  fire  1,  miss  5,  etc. 

5  fire  3,  miss  2  ;  fire  3,  miss  2,  etc. 
fire  2,  miss  2 ;  fire  2,  miss  2,  etc. 
fire  3,  miss  3  ;  fire  1,  miss  1,  etc. 

,,  „  ,      ,    (    fire  7,  miss  1  :  fire  8,  miss  2,  etc. 
Pull  load    '  '  '  '  ' 


)ad   j 


fire  8,  miss  1  ;  fire  8,  miss  1,  etc. 


If  the  engine  is  running  with  a  steady  load  the  firing 
cycle  may  repeat  itself  for  a  period  of  an  hour  or  longer ; 
then  it  may  change  to  some  other  cycle.  At  such  times  as 
the  governor  is  above  a  certain  level,  the  gas  intake  valve  is 
not  allowed  to  open,  and  the  charge  drawn  in  consists  of  air 
only. 

If  the  engine  runs  on  a  firing  cycle  of  fire  5,  miss  2,  etc., 
it  will  be  noticed  that  the  firing  card  after  the  two  misses 
will  be  larger  than  the  others.  This  is  due  to  the  fact  that 
during  the  two  miss  periods  just  preceding  the  firing  stroke 
the  cylinder  has  been  filled  twice  with  air,  which  has  greatly 
diluted  the  carbonic  acid  gas  left  in  the  clearance  space  by 
the  last  charge  fired,  so  that  the  firing  charge  taken  in  im- 
mediately after  the  two  miss  periods  is  mixed  with  fresh  air. 

Should  the  engine  be  running  under  light  load  on  a  firing 
cycle  of  fire  2,  miss  5,  etc.,  it  is  probable  that  the  first  firing 
card  after  a  period  of  five  misses  would  be  smaller  than  the 
second.     The  cooling  of  the  cyUnder  during  the  period  of 


90 


GAS  ENGINE  HORSE-POWER 


missing  has  prevented  any  great  amount  of  lieat  from  l)eing 
given  l)y  tlie  cylinder  to  the  new  charge  during  intake  and 
compression  and  consequently  the  lessened  pressure  at  the 
end  of  compression  causes  a  greater  reduction  in  the  mean 
effective  pressure  than  is  gained  liy  the  elimination  of  the 
carbonic  acid  gas  from  the  clearance  space. 

To  get  a  fair  average  card  the  pencil  of  the  indicator 
should  be  left  on  the  paper  during  a  complete  firing  cycle. 

The  spring  used  in  a  gas  engine  indicator  is  ordinarily 
one  hundred  and  fifty  or  two  hundred,  and  variations  of  two 
or  three  pounds  between  the  atmospheric  line  and  the  in- 
take and  exhaust  lines  are  hardly  noticeable  with  these 
springs  and  have  not  generally  been  considered  in  getting 
the  mean  effective  pressure  of  the  card.  This  resistance 
through  the  intake  and  the  exhaust  valves  should  be  taken 
into  account  in  getting  the  power  developed  by  the  engine. 
By  neglecting  these,  errors  of  from  ten  to  twenty  per  cent 
may  creep  into  the  work.  To  study  these  resistances  it  is 
necessary  to  use  a  light  spring  in  the  indicator.  This  s])ring 
may  be  protected  by  a  ferrule  or  stop,  furnished  with  the 
gas  engine  indicator,  which  prevents  the  piston  from  moving 
above  a  certain  level. 


Fig.  23a, 


GAS  ENGINE  HORSE-POWER 


91 


Fig.  236 


Cards  taken  witli  a  stiff  spring  and  with  a  light  spring 
are  shown  in  Figs.  2',h(  and  2'M.  The  straight  hne  at  the 
top  of  Fig.  2Sb  is  drawn  hy  the  pencil  while  the  indicator 
piston  is  against  the  stop.  The  line  D  C  is  the  exhaust  line 
and  C  A  is  the  intake.  The  distance  across  this  loop  will 
vary  from  four  to  eight  pounds,  according  to  the  make  of 
engine. 

The  card  shows  also  the  compression  and  expansion  of 
air  on  a  "  miss  "  stroke.  The  expansion  of  the  air  is  at  a 
pressure  slightly  lower  than  the  compression,  thus  making  a 
negative  loop.  It  will  be  noticed  that  the  last  end  of  the 
expelling  stroke  shows  a  higher  pressure  when  forcing  out 
air  than  when  forcing  out  burned  gas.  The  greater  velocity 
of  the  moving  column  of  burned  gas  in  the  exhaust  pipe 
exerts  more  of  an  aspirator  action  at  the  cylinder  at  the 
end  of  the  exhaust  stroke  and  so  causes  a  lower  pressure. 

To  obtain  the  mean  effective  j^ress^ire  for  an  engine  work- 
ing on  the  "  hit  and  miss  "  method  of  governing  :  Calculate 
the  mean  effective  })ressure,  using  compression  and  expan- 
sion lines  for  a  card  which  represents  the  mean  card  of  a 
complete  firing  cycle  of  working  and  missing  strokes.     Find 


92  GAS  ENGIISrE  HORSE-POWER 

from  the  card  taken  with  the  hght  s})ring  the  mean  pressure 
corresponding  to  the  loop  made  hetween  the  exhaust  and 
intake  lines  and  also  the  mean  pressure  representing  the 
distance  hetween  the  compression  and  the  expansion  lines 
during  a  miss  period  as  shown  l)y  A  B,  Fig.  23b.  This 
correction  is  to  he  applied  only  in  the  proportion  that  the 
misses  stand  to  the  firing  charges. 

Suppose  the  M.  E.  P.  as  figured  from  the  card  taken 
with  stiff  spring,  neglecting  the  loops  at  the  hottom  of  the 
card,  was  89  pounds.  Assume  the  hottom  loop  to  amount 
to  7  pounds.  Assume  the  air  loop  to  amount  to  .H  jjounds, 
and  call  the  firing  cycle  fire  5,  miss  2,  etc.  The  correct 
M.  E.  P.  is  89  -  7  —  (I  X  3)  =  80.8  ;  if  the  value  89 
had  heen  taken  for  M.  E.  P.,  the  error  in  the  power  cal- 
culation would  have  l)een  over  ten  per  cent.  Suppose  the 
cycle  had  heen  fire  2,  miss  5,  etc.,  and  other  values  the  same 
as  above.  The  correct  M.  E.  P.  =  89  —  7  —  (f  X  3)  =  74.5  ; 
hy  neglecting  these  loops  an  error  of  19  per  cent  would 
result. 

If  the  engine  fires  every  fourtli  stroke  and  governs  hy 
throttling  the  charge,  it  is  even  more  important  than  in  the 
})revious  case  to  get  the  cards  with  a  light  spring. 

After  obtaining  the  correct  M.  I"].  P.,  the  H.  P.  of  a  gas 
engine  is  figured  by  multiplying  the  area  of  the  piston  in 
square  inches  l)y  tlie  INI.  E.  P.  and  by  the  nundjer  of  feet 
traveled  by  the  piston  jjer  minute  during  ivorking  strokes, 
and  dividing  by  33,000. 

An  engine  governing  by  "■  hit  and  miss  "  nuist  have  some 
form  of  positive  counter  or  indicator  attached,  so  as  to  give 
the  number  of  explosions  in  a  certain  time. 

Engines  frequently  give  troulde  l)y  back  firing.  This  is 
in  some  cases  due  to  the  fact  that  tlie  mixture  is  still  bui'u- 
ing  in  the  cylinder  at  the  time  the  exhaust  valve  closes  and 
the  new  charge  enters  ;  in  other  cases  a  long  cored  hole,  a 
port  passage  or  an  indicator  pipe   may  hold  a  burning  mix- 


GAS  ENGINE  EFFICIENCY  93 

ture  all  through  the  exhaust  stroke  and  up  to  the  time  the 
fresh  charge  enters.  This  is  more  apt  to  be  true  with  slow 
Imrning  mixtures,  which  are  weak,  than  with  rich  mixtures. 
In  some  instances  the  indicator  piping  has  had  to  l)e  made 
of  snuiller  size  and  an  indicator  with  a  very  small  piston 
used,  in  order  to  prevent  this  firing  of  the  incoming  charge. 
The  theoretical  efficienc^i  of  a  four-cycle  gas  engine  is 

where  2\  is  the  absolute  pressure  at  the  l)eglnning  of  com- 
pressionj^y^  i^  the  absolute  pressure  at  the  end  of  compression 
and  A-  is  the  ratio  of  the  specific  heats  of  the  unbui-ned 
mixture  at  constant  pressu.re  and  at  constant  volume. 

Tivo-eycle  engines.  An  indicator  with  light  spring  shoidd 
be  attached  to  the  crank  case  or  compression  chamber  of 
the  snuill  two-cycle  engines  in  addition  to  that  on  the  work- 
ing cylindei'.  The  work  of  compression  in  the  crank  case 
is  to  be  deducted  from  that  shown  Ijy  the  working  cylinder. 
Large  two-cycle  engines  compress  the  gas  and  air  in  sepa- 
rate com])ressors. 

ACTUAL  THERMAL  EFFICIENCY  OF  A  GAS  ENGINE 
Tests  made  on  large  gas  engines  show  tliat  of  the  heat  of 
cond)Ustiou  of  the  gas  supjilied,  about  forty  per  cent  is  carried 
off  in  the  jacket  water,  about  thirty-live  per  cent  goes  off  in 
the  exhaust,  and  only  al)out  twenty-five  j)er  cent  is  converted 
into  work,  as  shown  l)y  the  card. 

Kxumple.  A  small  gas  engine  uses  22  cubic  feet  of  city 
gas  per  1.  H.  P.  per  hour.  The  gas  has  a  heating  value  of 
TOO  B.  t.  u.  per  cubic  foot.  The  heat  units  sujiplied  i)er 
miimte     are    — —  =  257 ;     a      horsepower      is     33,000 

foot-i)ounds  i)er  minute,  ecruivalent  to  ^^Wr-  =  42.42  B.  t.  u. 

'  ^  ^  7<S 

The  thermal  efficiency  per  I.  H.  P.  is  -^^  =  0.165,  or  10.5 
per  cent. 


CHAPTER  X 
THE  HYPERBOLIC  CURVE 

This  curve  is  fi'e(|uently  applied  to  indicator  diagrams 
for  the  purpose  of  comparing  it  with  the  expansion  curve, 
as  drawn  by  the  indicator,  and  if  it  coincides  pretty  nearly, 
this  fact  may  generally  he  taken  as  evidence  tending  to 
show  that  the  steam  and  exhaust  valves  of  the  engine  are 
properly  closed  and  the  piston  tight. 

Without  going  into  any  discussion  regarding  condensa- 
tion and  re-evaporation  in  steam  engine  cylinders,  it  is  a 
well  known  fact  that  indicator  diagrams,  taken  from  large 
engines,  properly  made  and  in  good  order,  show  expansion 
curves  which  are  close  approximations  to  the  hyperbola. 

Before  this  curve  can  be  drawn,  it  is  necessary  to  ascer- 
tain the  capacity  of  the  clearance  or  waste  room  :  that  is, 
all  the  space  between  the  cylinder  heads  and  the  piston  at 
each  dead-center,  including  the  counterbore  and  the  ports 
up  to  the  face  of  the  closed  valves. 

There  are  several  ways  of  finding  tliis :  one,  by  direct 
calculation  from  sectional  drawings,  when  accurate  draw- 
ings can  be  obtained ;  another,  by  putting  the  engine  at 
dead-center  with  valves  closed,  and  then  filling  the  clear- 
ance space  with  water,  which  has  been  carefully  weighed  in 
a  convenient  vessel,  then  weighing  what  is  left.  The  dif- 
ference between  the  weight  of  the  whole  and  the  remainder 
is  the  weight  of  water  required  to  fill  the  clearance  space. 
From  this  the  number  of  cubic  inches  occvipied  by  the  water 
may  be  computed.  At  ordinary  temperatures  (60°  to 
75°  F.),  for  all  practical  purposes,  we  may  call  the  weight 
of  one  cubic  inch  of  water  0.036  pounds  and  27.8  cubic 
inches  of  water  equal  to  one  pound.     Then  the  nmnber  of 

94 


THE   HYPERBOLIC   CURVE 


95 


pounds  of  water  divided  by  0.036  or  multiplied  by  27.8 
will  give  the  number  of  cubic  inches.  If  accurate  scales 
for  weighing  the  water  are  not  at  hand,  it  can  be  carefully 


k-  \---/6>y H--7^ 


Clearance  0.04  of  Stroke 

Fig.  24 

measured  in  a  quart  or  pint  measure  and  the  number  of 
cubic  inches  found  directly.  A  gallon  contains  231  cubic 
inches,  a  quart  57.75,  and  a  pint  28.875  cubic  inches. 

The  volume  of  the  clearance  will  rarely  be  the  same  at  the 
two   ends    of    the  cylinder,  therefore  the  number  of  cubic 


96  THE   HYPERBOLIC   CURVE 

inches  in  the  clearance  at  each  end  nui.st  he  divided  hy  the 
net  area  of  the  piston  at  its  own  end :  that  is,  the  number 
of  cubic  inches  in  the  clearance  at  the  end  nearest  the  crank 
must  be  divided  by  the  number  of  square  inches  in  the 
cross-section  of  the  cylinder,  less  the  number  of  square 
inches  in  the  cross-section  of  the  piston-rod  ;  and  the  number 
of  cubic  inches  in  the  clearance  at  the  end  farthest  from  the 
crank  must  be  divided  by  the  numl)er  of  square  inches  in 
the  cross-section  of  the  cylinder.  The  quotient  in  each  case 
will  be  the  length  of  clearance  at  the  resjiective  ends  of  the 
cylindei-,  expressed  in  ii>ches.  In  this  instance  (Fig.  24)  it 
is  found  to  be  0.16  of  an  inch. 

It  is  convenient  to  have  the  length  of  the  clearance 
expressed  as  a  fraction  of  the  piston  displacement  or  stroke 
of  the  piston.  To  obtain  this  fraction,  divide  the  number 
of  cubic  inches  in  volume  of  clearance  by  the  number  of 
cubic  inches  in  the  volume  swept  through  by  the  jjiston  at 
each  end  separately,  taking  care  to  allow  for  the  volume 
occupied  at  one  end  by  the  piston-rod,  and  the  quotient  will 
be  the  decimal  fraction  that  the  clearance  space  is  of  the 
volume    swept    through    by    the    piston. 

Fig.  24  illustrates  a  good  method  for  locating  points  in 
the  hyperl>ola  through  which  the  curve  may  be  drawn. 

First,  draw  the  zero  line  V,  at  the  proper  distance,  viz., 
14^^  pounds  by  the  scale,  below  and  parallel  with  the 
atmospheric  line  ;  next,  draw  the  clearance  line  O,  as  com- 
puted, 0.16  of  an  inch  from  the  end  of  the  diagram ;  next, 
locate  the  point  of  cut-ofB  X,  and  draw  the  perpendicular 
line  numbered  3  through  it ;  next,  divide  the  space  between 
this  line  and  the  clearance  line  into  three  equal  parts ;  then, 
taking  one  of  these  parts  for  a  measure,  point  off,  on  the 
vacuum  line,  eqiad  spaces  toward  the  left  hand  until  one  or 
more  falls  beyond  the  end  of  the  diagram  as  shown,  and 
erect  perpendicular  lines  from  each  ])oint.  These  lines  are 
called  ordinates  and  numbered  consecutively  1,  2,  3,  4,  etc., 


THE    HYPERBOLIC   CURVE  97 

beginning  with  the  one  next  to  the  clearance  line.  It  is 
well  to  bear  in  mind  the  fact  that  vertical  distance  on  a 
diagram  represents  pressure  and  horizontal  distance  tiolimie. 

In  this  case  we  have  started  the  hyperljola  from  the  point 
of  cut-ofE  X,  and  its  course  is  indicated  by  the  short  lines 
drawn  through  the  ordinates  a  little  above  the  actual  curve, 
with  their  calculated  pressures  written  above  ;  the  actual 
pressures  of  the  expansion  curve  are  written  lielow  it.  The 
properties  of  the  hyperbola  are  such,  that  if  the  distance  of 
the  point  X  from  the  clearance  line  O  be  multiplied  by  the 
height  of  X  from  the  zero  line  V,  the  height  of  any  other 
point  in  the  curve  can  be  found  by  dividing  this  product  by 
its  distance  from  the  clearance  line.  And  on  this  principle 
we  proceed  to  locate  points  on  the  ordinates  through  which 
our  hyperbola  will  run. 

We  find  the  pressure  at  the  point  of  cut-off  to  be  121 
pounds  with  a  volume  which  we  call  3,  because  there  are 
three  spaces  or  volumes  between  it  and  the  clearance  line. 
Then,  121  X  3  =  363,  which  is  our  dividend  for  all  the 
other  volumes.  Therefore,  the  height  at  which  the  hyper- 
bola will  cut  ordinate  4  will  be  determined  by  dividing  363 
by  4,  which  is  90.8  (it  is  unnecessary  to  carry  the  division 
beyond  one  decimal)  ;  and  at  ordinate  5,  72.6  ;  at  ordinate 
6,  60.5 ;  and  so  on  to  the  end.  At  ordinate  12  we  find 
that  the  hyperbolic  and  the  actual  curves  practically  coincide. 
In  like  manner  we  may  extend  the  curve  to  the  right : 
363  -f-  2  =  181  pounds,  which  would  be  the  pressure  if  the 
steam  were  compressed  up  to  2  volumes.  If  desired,  the  hyper- 
bolic curve  can  be  started  just  before  the  point  of  release 
and  projected  in  the  opposite  direi^tiou  by  the  same  method. 

Instead  of  using  figures  which  stand  for  pressures  or 
volumes  of  steam  to  locate  the  liy])erbola,  as  in  this  instance, 
the  distances  from  the  base  and  perpendicular  lines  of  any 
])oint  niay  be  expressed  in  inches  and  decimal  parts,  with 
the  same  result. 


98 


METHODS  OF  FINDING  THE  HYPERBOLA 


A  quick  way  to  draw  the  hyperbola  is  to  take  the  whole 
distance  between  ordinate  3  and  the  clearance  line,  (Fig.  24), 
as  a  measure,  and  set  off  equal  spaces  to  the  left  as  be- 
fore directed.  Then  we  would  have  but  four  ordinates  and 
would  niuiiber  them  as  follows  :   1  at  3d,  2  at  6th,  3  at  9th, 


Fig.  25 


and  4  at  12th.  At  1  we  would  have  a  pressure  of  121 
pounds  ;  at  2,  121  pounds  -r-  2  =  60.5  ;  at  3,  121  pounds 
4-  3  =  40.3  ;  and  at  4,  121  pounds  -^  4  =  30.25. 


METHODS  OF  FIXDIXG  THE  HYPERBOLA  99 

As  a  general  rule,  the  near  approximation  of  the  expan- 
sion curve  to  the  theoretical  or  hyperbolic  curve  may  be 
taken  as  evidence  of  good  conditions  but  should  not  be 
accepted  for  a  certainty,  unless  all  the  known  facts  and 
conditions  tend  in  the  same  direction. 

GEOMETRIC  METHOD  OF  FINDING  THE  HYPERBOLA 

The  hyperbola  may  be  found  by  following  the  directions 
given  below,  in  connection  with  Fig.  25.  A  is  the  atmos- 
jiheric  line  ;  Z  the  zero  line,  or  line  of  no  pressure ;  B  the 
line  of  boiler  pressure,  and  C  the  clearance  line.  Locate 
the  first  point  in  the  hyperbola  at  the  point  of  release  X 
and  draw  tlie  vertical  line  X  E.  Then  draw  diagonal  line, 
E  H  ;  then,  from  X,  draw  horizontal  line  5  to  its  intersec- 
tion w4th  E  H,  through  which  draw  vertical  line  F  O.  Now 
mark  off  points  between  O  and  E  as  1,  2,  3,  4  —  exact  spa^ 
cing  is  unnecessary  —  and  from  these  points  draw  diagonal 
lines  to  H  and  vertical  lines  down  to,  or  a  little  below,  the 
actual  curve.  Now  draw  horizontal  lines  6,  7,  8,  and  9 
from  the  points  of  intersection  in  the  line  F  O,  of  the 
diagonal  hnes  H  4,  H  3,  H  2,  and  H  1  respectively ;  and 
the  points  where  these  lines  cross  the  vertical  lines,  1,  2,  3, 
and  4,  in  connection  with  points  X  and  O,  are  the  points 
through  which  the  hyperbola  should  be  drawn,  as  shown  by 
the  dotted  curve. 

ANOTHER  METHOD  OF  FINDING  THE  HYPERBOLA 

Through  the  point  of  release  h,  draw  any  line  as  a  B  and 
make  A  B  equal  to  (/  h,  as  shown  in  Fig.  26.  Then  draw 
any  other  line  as  c  D  and  make  c  d  equal  to  A  D  ;  then  d 
wall  be  a  point  in  the  hyperbola  passing  from  h  to  A,  as 
shown  by  the  dotted  curve.  By  drawing  a  number  of  lines 
through  A  and  following  the  same  method,  we  can  find  as 
many  points  in  the  hypei'bola. 


100 


MJETHODS  OF  KIXDING  THE  HYPERBOLA 


q  f^ 


Fig.  26 


PART  II 


PART  II 


APPLICATIONS 

The  steam  engine  indicator  may  be  used  for  a  great  many 
purposes  besides  those  mentioned  in  the  preceding  chapters. 
The  a2>phcations  are  so  varied  that  the  cases  selected  and 
illustrated  in  these  pages  show  only  a  few  of  those  which 
seem  to  be  most  useful. 

I.  Valve  Setting 
If  the  cards  taken  from  the  two  ends  of  the  cylinder  re- 
semble Figs.  27  or  28,  the  eccentric  has  too  little  angular 


Fig.  27 


advance  and  must  be  turned  ahead  ;  in  the  case  of  an  engine 
giving  cards  shown  by  Fig.  27,  moving  the  eccentric  ahead 


Fig.  28 
103 


104  APPLICATIOSrS 

5°  to  10°  would  probably  be  sufficient,  while  with  Fig.  28, 
20°  to  30°  would  be  ncLMled. 

If  the  cards  from  both  ends  resemble  Figs.  29  or  30,  the 
eccentric  has  too  much  anjrular  advance  and  should  be  turned 


Fig.  29 


back  a  small  amount  for  Fig.  29,  and  a  much  larger  amount 
for  Fig.  30. 

Cards  similar  to  Figs.  29  and  30  are  obtained  at  early 


Fig.  30 

cut-off  from  most  single  valve  high  speed  engines  with  fly- 
wheel governors. 

A  plain  slide  valve  engine,  or  an  engine  with  piston  valve, 
taking  steam  on  the  outside,  will  give  cards  like  Figs.  31  and 
32  when  the  valve  spindle  is  too  long,  the  eccentric  being  in 
the  right  place. 

The  effects  of  lengthening  the  valve  spindle  are  (1)   to 


APPLICATIONS 


105 


increase  the  steam  lap  on  the  head  end,  delaying  admission 
and  hastening  cut-off  on  this  end  ;  (2)  to  decrease  the 
steam  lap  on  the  crank  end,  hastening  admission  and  delay- 
ing cut-off ;  (3)  to  decrease  the  exhaust  lap  on  the  head  end, 
hastening  release  and  delaying  compression ;  and  (4)  to 
increase  the  exhaust  lap  on  the  crank  end,  delaying  release 
and  hastening  compression. 


Fig.  31 


If  the  valve  spindle  is  too  long  and  at  the  same  time  the 
eccentric  has  too  little  angular  advance,  or  is  set  too  far 
hack,  the  cards  from  the  engine  will  he  similar  to  Figs. 
33  and  34. 


Fig.  32 


If  the  eccentric  is  set  too  far  ahead  and  the  spindle  is  too 
long,   the   appearance   of    the   cards   may   he   predicted   by 


106 


APPLICATIONS 


Head  End 


Fig.  33 

combining  the  effects  shown  by  Figs.  29  or  30  with  Figs. 
31  and  32. 

2.    Steam  Chest  Cards 

A  steam  engine  indicator  may  be  connected  to  the  steam 
chest  of   the   engine   and   cards   taken  simnltaneously  with 


Crank  End 


Fig.  34 


cards  from  the  cyhnder,  botli  indicators  being  attached  to 
the  same  reducing  motion. 

For  comparison,  it  is  convenient  to  superimpose  the  chest 
card  on  the  cyhnder  card,  as  has  been  done  in  Fig.  35. 

The  steam  chest  card  A  B  C  D  E  C  A,  Fig.  35,  is  for  one 
revolution.  If  the  steam  pipe  and  steam  port  leading  from 
the  steam  chest  to  the  cylinder  are  large   enough,  there  will 


APPLICATIONS 


107 


be  no  appreciable  drop  in  pressure  between  the  boiler  and 
tlie  steam  chest,  or  between  the  chest  and  the  cylinder.  If, 
however,  a  chest  card  similar  to  that  shown  by  the  full  line 
is  obtained,  the  steam  pipe  is  too  small.  This  is  shown  by 
the  fact  that  the  di'op  from  boiler  pressure  A  appears  in  the 
steam  chest  card  while  the  drop  between  the  steam  chest 
and  the  cylinder  is  slight. 


Fig.  35 


If  the  clie.st  card  showed  a  slight  drop  in  pressure,  as 
indicated  by  the  dotted  line  AG,  it  would  mean  that  the 
steam  port  leading  from  the  chest  to  the  cylinder  was  too 
small. 

A  chest  card  sliown  by  the  line  AH  would  mean  that 
both  the  steam  pl])e  and  the  steam  ports  were  too  small. 

Sometimes  the  pressure  at  C  is  greater  than  boiler  pres- 
sure, A.  Tliis  results  from  the  sudden  checking  of  the 
velocity  of  the  steam  in  the  pipe  supplying  the  engine. 

3.    The  Eccentric  Card 

Near  the  ends  of  the  stroke  of  an  engine  the  crank  turns 
through  a  considerable  number  of  degrees  without  giving 
much  motion  t(»  the  cross-head. 


108 


APPLICATIONS 


On  account  of  this  fact  the  indicator  card  taken  in  the 
ordinary  way  is  of  httle  vahie  in  investigating  any  peculi- 
arities which  may  he  noticed  at  or  near  the  ends  of  the 
stroke. 


Fig.  36 

If,  however,  the  drum  motion  he  taken  from  the  eccen- 
tric, which  is  ordinarily  a  little  over  90°  ahead  of  the  crank, 
the  compression  and  admission  lines  and  the  line  at  release 
will  he  spread  out  at  the  center  of  the  diagram,  while  the 
expansion  and  exhaust  lines  Avill  he  shortened  and  a2)pear 
at  the  ends  of  the  cards. 


Fig.  37 
Fig.  37  represents  a   good   steam   card,  and   Fig.  38  an 
eccentric  card. 


APPLICATIOXS  109 

The  cards  are  lettered  at  admission,  cut-off,  release,  and 
compression  with  the  letters  A,  B,  C,  D,  respectively. 

It  will  be  noticed  on  the  eccentric  card  tliut  tlie  line  DA 
is  a  reverse  curve. 


Fig.  38 

On  the  card  taken  from  an  engine  with  throttling 
governor,  Fig.  36,  a  peculiar  drop  near  the  end  of  com- 
jiression  is  found.  This  is  due  partly  to  a  leakage  of  steam 
from  the  cleaiance  space  over  the  bridge  into  the  exhaust 
and  partly  to  a  slight  amount  of  condensation.  Tliis  drop 
appears  on  the  eccentric  card  as  in  the  dotted  line. 

4,  Steam  Cards  from  a  Westinghouse  Air  Brake  Pump,  or  from 
a  Wet  Air  Pump  with  Surface  Condenser 

In  the  diagi'am  shown  by  Fig.  39  the  piston  starts  at  the 
left  and  moves  towards  the  right.  As  the  work  ojiposed  to 
the  steam  piston  by  the  air  piston  is  but  trifling  during  the 
first  part  of  the  stroke,  the  steam  piston  "  runs  away  from 
the  steam,"  causing  the  drop  in  pressure  shown. 

Near  the  end  of  the  stroke  the  extra  work  opposed  to  the 
steam  piston  l)y  the  air  piston  causes  it  to  slow  do^\Ti,  and 
then  steam  has  time  to  fill  the  cylinder  at  nearly  boiler 
pressure.  On  the  return  stroke  the  piston,  during  the  first 
part  of  its  stroke,  travels  so  fast  that  the  steam  cannot  be 
freely  exhausted.      Dvu-ing  the   latter    part    of    the   stroke. 


110 


APPLICATIONS 


liowever,  when  the  piston  slows  up,  the  jjressure  drops 
nearly  to  that  in  the  exhaust  pipe,  as  shown  hy  the  lower 
hue  of  Fiir.  39. 


Fig.  39 

A  casual  inspection  of  Fig.  39  might  lead  to  the  con- 
clusion that  the  greatest  effective  pressure  on  the  piston  was 
at  the  left-hand  end  near  the  beginning  of  the  stroke.  This 
is  not  the  case,  as  may  he  seen  hy  constructing  what 
is  called  the  stroke  card,  shown  hy  Fig.  40,  and  again  by 
Fig.  46.  Assvmiing  that  the  piston  has  a  tail-rod  so  that  the 
area  of  the  head  end  of  the  piston  is  the  same  as  the  area 
of  the  crank  end,  the  effective  push  per  square  inch  on  the 
piston  at  any  time  is  the  difference  of  pressure  on  the  two 
sid-es  at  that  time.      If  now  the  steam  line  of  the  card  from 


Fig.  40 


APPLICATIONS  111 

the  head  end  he  comhined  with  the  hack  pressure  line  from 
the  card  of  the  other  end,  we  get  a  diagi'ani  known  as  the 
Stroke  Card,  sometimes  called  the  True  Card,  which,  hy  its 
distance  between  lines,  gives  the  effective  pressure  per 
square  inch  on  the  piston  at  any  point.  Such  a  diagram  is 
shown  hy  Fig.  40  for  the  Air  Brake  Card.  It  A^dll  be  noted 
that  the  greatest  effective  push  on  the  piston  comes  at  the 
riffht-hund  end,  not  the  left. 

If  the  two  ends  of  the  steam  piston  have  not  the  same 
area,  the  pressures  from  one  indicator  card  may  be  multi- 
plied by  the  ratio  of  the  two  areas,  before  plotting,  in  order 
to  reduce  to  the  same  basis  for  comparison. 

5.  Air  Compressor  Cards 

Figs.  41  and  42  are  respectively  from  an  air  compressor 
and  from  the  air  end  of  a  certain  type  of  air  pump. 

The  irregiilarities  in  the  delivery  line  of  Fig.  41  are  due 
to  the  vibrations  of  the  delivery  valve.     The  slight  drop  at 


Fig.  41 

the  beginning  of  ail'  intake  results  from  resistance  to  open- 
ing offered  by  the  suction  valves. 

The  air  pumj)  pumps  a  mixture  of  water  and  air.  On 
account  of  the  large  clearance  the  curves  are  much  less  steep 
than  in  the  case  of  the  air  compressors. 


112 


APPLICATIONS 


Fig.  42 


6.  Gas  Engine  Cards 

Figs.  43  and  44  are  from  an  Otto  Gas  Engine.  Fig.  44 
has  the  firing  delayed  till  the  end  of  the  stroke,  and  shows 
plainly  the  effect  of  not  having  a  "  lead  "  on  the  firing 
spark. 

Engines  working  on  the  Otto  cycle  can  have  only  one 
working  stroke  in  four,  and  as  many  of  these  engines  work 
on  the  "  hit  and  miss  "  principle,  in  figixring  the  horsepower 
from  the  cards  it  is  necessary  to  note  the  actual  mmiher  of 
explosions  per  minute. 

Starting  at    exhaust  on   the   right-hand  end,   the   piston 


D 


Fig.  43 


APPLICATIOlSrS 


113 


moves  to  the  left,  along  AB,  and  drives  out  the  burned 
gases  through  the  exhaust  valve  ;  next  the  exhaust  valve 
closes,  and  as  the  piston  moves  to  the  right,  gas  and  air  are 
drawn  in,  along  BA,  the  mixture  being  regulated  by  the 
opening  of  the  gas  inlet,  so  as  to  get  the  proper  ratio  of  gas 
to  air.  On  the  third  stroke  this  mixture  is  compressed, 
along  AC,  and  just  before  the  piston  reaches  the  end  of  the 
stroke  the  mixture  is  fired ;  the  hot  gases  expand  dm-ing  the 
fourth  stroke,  DA. 


B^ 


Fig.  44 

If  the  engine  is  up  to  speed  and  gas  is  not  admitted  by 
tlie  governor,  the  cylinder  is  filled  with  air  on  the  fiUing 
stroke ;  this  air  is  compressed  on  the  third  stroke  and 
expands  back  again  along  nearly  the  same  line  on  the 
fourth  stroke. 


Fig.  45 


114 


APPLICATIONS 


7.    Ericsson  Hot  Air  Engine  Cards 

Fig.  45  is  from  an  Ericsson  hot  air  engine.  This  is  taken 
with  a  10  pound  spring.  As  there  are  no  valves  in  this 
engine,  the  same  air  being  alternately  heated  and  cooled,  it 
is  impossible  to  get  sharp  corners  on  the  card. 

8.   Stroke  Card 

Fig.  46  represents  a  stroke  card  from  a  Corliss  engine. 
This  is  constructed  as  explained  in  conftection  with  Fig.  40. 


Fig.  46 


Near  the  end  of  the  stroke  the  pressure  on  the  opposing 
side  of  the  piston  is  greater  than  that  on  the  pushing  side, 
as  shown  by  the  part  cross-hatched.  During  this  short 
interval  the  fly  wheel  pulls  the  engine  over. 


Fig.   47 


APPLICATIONS 


115 


9.  Rotative  Effect 
The  total  pressure  on  the  piston-rod  at  any  point  may  be 
found  by  multiplying  the  pressure  measured  across  the 
stroke  card  at  that  point  by  the  area  of  the  piston.  Sup- 
pose the  total  pressure  on  the  piston-rod  at  the  position 
shown  in  Fig.  48  is  1,000  pounds.  Draw  the  line  P  to 
represent  this  pressure  at  some  assumed  scale,  say,  for 
example,  one  inch  representing  500  pounds.  Then  P  =  2 
inches  long. 


Fig.  48 


This  force  P  produces  a  push  along  the  connecting  rod 
and  a  downward  thrust  on  the  guides.  This  push  along  the 
rod  and  this  thrust  on  the  guides  may  be  found  by  making 
a  triangle  of  forces  as  sho^vn.  The  length  of  the  different 
sides  of  the  triangle  multiplied  by  500  gives  these  forces  in 
pounds. 

The  tlunist  in  the  connecting  rod  is  seen  to  be  greater 
than  P.  Tliis  thrust  at  the  cross-head  end  of  the  connecting 
rod  is  carried  to  the  crank  pin  where  it  may  be  separated 
into  two  forces,  one  force  R  at  right  angles  to  the  crank 
tending  to  produce  rotation,  and  another  force  along  the 
crank  making  a  compression  in  the  crank  casting. 

If,  now,  values  of  R  are  calculated  for  a  sufficient  num- 
ber of  points  and  plotted  on  a  line  wliich  represents  the 
development  of  the  crank  pin  circle,  a  diagram  of  rotative 
effect  hke  Fig.  49  is  obtained.  The  upper  half  comes  from 
one  stroke  card  and  the  other  half  from  the  other  stroke  card. 


116 


APPLICATIONS 


The  mean  rotative  effect  is  shown  by  the  clot  and  dash 
lines. 

The  amount  of  energy  stored  and  restored  by  the  fly 
wheel  during  a  stroke  is  represented  by  the  area  within 
the  curve  outside  of  the  dash  and  dot  line. 

In  tliis  discussion  it  has  been  assumed  that  the  entire 
pressure  on  the  piston  was  available  for  producing  rotative 
effect.  This  is  not  the  case,  however.  A  certain  amount 
of  this  pressure  is  used  up  at  the  beginning  of   the  stroke  in 


Fig.  49 


accelerating  the  piston,  piston-rod,  cross-head,  and  a  part  of 
the  connecting  rod.  As  these  are  brought  back  to  rest  at 
the  end  of  the  stroke,  as  much  energy  is  recovered  as  was 
lost  at  the  beginning.  The  dotted  line  on  Fig.  46  shows 
how  the  upper  Une  should  be  changed  to  make  allowance 
for  this,  in  the  case  of  a  low  speed  Corhss  engine.  On  a 
high  speed  engine  this  is  a  much  larger  factor,  as  may  be 
seen  in  Fig.  47.  In  this  figure  the  effective  pressure  per 
square  inch  available  for  producing  rotative  effect  is  shown 
by  the  area  cross-hatched. 


APPLICATIONS 


117 


10.  Explosive  Force  of  a  Mixture  of  Gas  and  Air 
Fig.  50  was   obtained  with  a  gas   engine   indicator  and  a 
tuning  fork.     The  mixture,  which  was  one  part  Boston  gas 


Fig.  50 

to  six  parts  air,  was  compressed  to  25  pounds,  as  shown  at 
the  left  of  the  diagram.  It  was  then  fired  by  a  spark,  and 
a  pressure  of  225  pounds  above  the  atmosphere  resulted. 
The  tuning  fork,  which  was  marking  on  the  paper  at  the 
same  time,  gave  a  means  of  estimating  the  time  required  to 
reach  maximum  pressure.  Each  wave  denotes  ^^  of  a 
second. 

This   explosion  was  /^  or  ^^  of   a   second   in   reaching 
maximmn  pressure. 


II.  Measuring  Water  Hammer 

Fig.  51  was  taken  from  a  4  incli  drive  pipe  90  feet  long, 
supplying   a  Rife   Hydraulic    Ram.     The   fall   of  water   to 


Fig.  51 


118 


APPLICATIONS 


tlie  ram  was  about  8  feet.  Beneath  the  card  a  wave  line 
drawn  by  a  tuning  fork  gives  a  means  of  measuring  time 
accurately.  The  maximum  pressure  is  320  pounds.  The 
recui'rence  of  figures  similar  to  the  fii'st,  but  with  rapidly 
decreasing  pressures,  seems  to  indicate  a  wave  traveUng 
back  and  forth  in  the  pipe.  The  air  which  is  carried  by 
the  water  no  doubt  has  sometliing  to  do  with  tliis. 

12.    Flather  Dynamometer 

A  form  of  dynamometer  built  by  Mr.  John  J.  Flather 
makes  use  of  a  steam  engine  indicator  for  measuring  power. 
Figs.  52   and   53   show  the   indicator   cards   taken   from   a 


Fig.  52 


Fig.  53 


dynamometer  attached  to  a  power  drill.  Fig.  52  was  taken 
with  a  sharp  driU  running  into  a  cored  hole  in  a  casting. 
The  hole  was  coated  with  rough  sand  and  the  drill  lost  its 
edge  rapidly,  when  it  gave  a  diagram  like  Fig.  53. 

This  dynamometer  consists  of  a  hollow  shaft  on  which  are 
two  pulleys,  one   tight  and  the  other  loose.     On   opposite 


Fig.  54 


APPLICATIONS 


119 


arms  of  the  tight  pulley  are  two  small  cylinders  which  are 
open  at  one  end.  The  cylinders  connect  through  pipes, 
at  the  closed  ends,  with  the  hollow  shaft.  Built  out  from 
the  arms  of  the  loose  pulley  are  two  studs  carrying  pistons 
which  fit  into  the  cylinders.  The  cylinders  are  filled  with 
oil,  as  is  also  the  hollow  shaft,  to  the  end  of  which  the  indi- 
cator is  attached.  The  loose  pulley  drives  the  tight  pulley 
through  its  pistons,  wliich  press  on  the  oil  in  the  cylinders 


Fig.  55 

carrie,d  hy  the  tight  pulley.  The  steam  engine  indicator 
records  this  pressure.  The  drmn  of  the  indicator  is  driven 
from  the  shaft  through  a  worm  and  wheel. 

13.    Pulsometer  Steam  Pump 

Figs.  54,  55,  56  are  taken  from  the  left  side,  the  right 
side,  and  the  air  chamber  of  a  pulsometer  steam  pump. 


Fig.  56 


These  cards  were  taken  at  the  same  time.  The  drums  of 
the  indicators  were  moved  at  the  same  uniform  rate  by 
means  of  gears  driven  by  a  line  of  shafting.  Fig.  57  shows 
the  combined  diagram,  giving  the  pressm-es  at  any  part  of 
the  pump  at  any  time. 


120 


APPLICATIONS 


The    line  AA    represents   the  atmospheric  line,  the  line 
W  that  corresponding  to  an  absolute  vacuum,  and  the  line 


-1-03  seconds 


V  ' 


Fig.  57 


V. 


PP  the  pressure  in  pounds  due  to  the  hydrostatic  head  the 
pimip  was  delivering  against.  The  shaded  portions  repre- 
sent deliveries  of"  water. 


PART  III 


PART  III 

CHAPTER  I 

PROPERTIES  OF  STEAM  AND  OF  PERFECT  GASES 

In  order  to  make  complete  calculations  of  an  engine  test, 
and  in  order  to  get  as  much  information  as  is  possible  from 
the  cards,  it  is  necessary  to  understand  the  properties  of 
saturated  steam  and  to  be  aide  to  make  intelligent  use  of 
tables  or  plots  giving  such  properties. 

It  is  not  the  intention  to  give  here  any  lengthy  discussion 
of  thermodynamics,  and  oidy  such  parts  of  that  subject  will 
be  touched  as  bear  directly  on  work  depending  upon  the 
indicator  card  or  the  solution  of  practical  problems  such  as 
may  come  to  an  engineer  in  charge  of  a  plant. 

Pmssicres.  The  pressure  of  the  atmosphere  is  usually 
taken  as  14.7  pounds  per  square  inch.  This  corresponds  to 
a  corrected  reading  on  the  barometer  of  29.92  inches. 
Steam  gages  are  made  to  read  pressures  above  the  atmos- 
l)here ;  therefore  to  get  what  is  called  the  absolute  pressure, 
the  pressure  of  the  atmosphere  must  be  added  to  that  shown 
by  the  gage. 

A  barometric  reading  in  inches  of  mercury  may  be  re- 
duced to  pounds  pressure  on  the  square  inch  by  multiplying 
its  corresponding  reduced  height  at  32°  F.  by  0.491. 

The  reduced  height  for  a  barometer  having  a  brass  scale 
may  be  calculated  from  the  following : 

[1  +  0.0000102  {t  —  62)]  X  h 
1  +  0.000101  {t  —  32) 

where  h  is  the  observed  height  in  inches  and  t  is  the  Fahren- 
heit tem])erature  at  the  barometer. 

123 


124        '  PROPERTIES  OF  STEAM  AND  PERFECT  GASES 

To  measure  pressure  below  the  atmosphere,  a  vacuum 
gage  or  a  glass  U  tube  filled  with  mercury  may  be  used.  It 
is  customary  to  quote  the  vacuum  in  inches  of  mercury  in- 
stead of  in  pounds.  If  the  barometer  stood  29.9  inches 
a  vacuum  of  2G  inches  would  mean  that  there  was  an  abso- 
lute pressure  of  3.9  inches,  or  (3.9  X  0.491)  pounds. 

All  pressures  as  given  in  plots  or  in  tables  of  the  proper- 
ties of  saturated  steam  are  absolute  pressures. 

Specific  i^t'^^'^^fo'^  and  sjiccific  volume.  Specific  pressure 
is  absolute  pressure  on  the  square  foot.  Specific  volume  is 
the  volume  of  one  pound. 

The  specific  volume  of  water  is  g-jrr^  0.016  cubic  feet, 
62.4  pounds  ])eing  the  weight  of  a  cubic  foot  of  water  at  62°. 

The  volume  of  a  i)ound  of  dry  steam,  represented  by  the 
letter  s,  varies  with  the  pressure. 

The  Brtttsh  thermal  unit,  B.  t.  u.,  is  the  amount  of 
heat  necessary  to  raise  one  pound  of  water  from  62°  F.  to 
63°  F. 

The  heat  of  the  liquid  is  the  amount  of  heat  expressed 
in  B.  t.  u.  necessary  to  raise  one  pound  of  water  from  32° 
to  the  temperature  desired. 

If  the  specific  heat  of  water  was  unity  throughout  the 
entire  range  of  temperature,  the  heat  of  the  Hquid  would  be 
32  less  than  the  temperature. 

The  specific  heat  is  slightly  above  unity  at  some  temperar 
tiu'es,  and  slightly  below  unity  at  other  temperatures. 

The  heat  of  the  htpiid  is  represented  by  the  letter  q. 

Relation,  of  jjressure  and  temperature  of  saturated  steam: 

Regnault  found  that  the  temjjerature  of  steam  depended 
upon  the  pressure  ;  that  the  temperature  of  the  steam,  if  it 
was  not  su])erheated,  was  exactly  the  same  as  that  of  the 
water  in  contact  with  it. 

Particles  of  water  may  float  in  steam  the  same  as  fog 
floats  in  the  air.  This  does  not  affect  the  tenqjerature  of 
the  steam. 


PROPERTIES  OF  STEAM  A2fD  PERFECT  GASES  125 

Total  latent  heat  or  heat  of  vaporization  (represented 
by  /•)  : 

If  a  pound  of  water  at  32°  is  heated  up  to  the  boihng 
point  at  atmospheric  2)ressiu'e,  180.3  lieat  units  (the  vahie  q 
of  the  lieat  of  the  Uquid),  wall  he  consumed  in  raising  the 
tem})erature  from  32°  to  212°.  If  now  heat  is  added,  the 
water  Avill  gra(hially  go  off  as  steam.  To  entirely  vaporize 
this  i)oun(l  969.7  B.  t.  u.  will  he  needed.  This  969.7  B.  t.  u. 
is  the  heat  of  vaporization  at  this  pressure.  It  is  often 
called  the  total  latent  heat. 

The  heat  of  vaporization  is  different  at  different  pressures. 

The  total  heat  at  any  jiressure  (represented  hy  the  Greek 
letter  \  called  lambda)  is  the  amomit  of  heat  necessary  to 
raise  a  pound  of  water  from  32°  to  the  temperature  corre- 
sponding to  the  pressure  and  to  tlien  entirely  vaporize  the 
water  at  this  temperature  and  imder  the  constant  pressure. 

It  is  evidently  equal  to  the  smn  of  q  and  r,  the  heat  of 
the  li(piid  and  the  total  latent  heat. 

Until  recently  the  values  of  X-  as  determined  hy  Regnault 
were  used,  although  they  were  known  to  he  somewhat  in 
error  ;  recently,  however,  Mr.  H.  N.  Da\as  has  deduced 
correct  values  of  the  total  heat  hy  making  use  of  the  experi- 
mental data  at  hand,  mainly  that  of  Grindley,  of  Griess- 
nian,  and  of  Knoblauch,  all  three  of  whom  were  at  Avork  on 
the  determination  of  the  values  of  the  specific  heat  of 
superheated  steam. 

Heat  equivalent  of  external  work  and  lieat  equivalent  of 
internal  ivork  : 

As  water  passes  into  steam  at  constant  pressvire  and  at 
constant  temperature,  we  have  seen  that  the  heat  of  vapor- 
ization r  is  re(][uired. 

This  value  r  is  made  up  of  two  parts.  One  part,  the 
heat  equivalent  of  the  external  work,  can  be  calculated. 

The  other  part,  the  heat  equivalent  of  the  internal  work, 
is  obtained  by  subtracting  the  first  from  r. 


126  PROPERTIES  OF  STEAM  AJS'D  PERFECT  GASES 

The  following  examjile  will  illustrate  the  method  of  calcu- 
lating the  heat  equivalent  of  the  external  work. 

Suppose  one  pound  of  water  at  32°  to  be  placed  in  the 
bottom  of  a  vertical  cylinder  of  one  square  foot  piston  area. 
Let  the  piston  be  weighted  so  that  together  with  the  atmos- 
pheric pressure  there  is  a  load  of  100  pounds  per  square 
inch  on  the  piston. 

If  heat  is  added  to  the  water,  vaporization  will  not  begin 
till  a  temperature  of  327. 8G°  F.  is  readied.  As  vaporiza- 
tion takes  place  the  piston  rises  in  the  cylinder. 

When  all  the  water  has  been  made  into  steam,  the  piston 
will  stand  4.432  feet  above  the  bottom  of  the  cylinder. 

The  pound  of  water  occupied  0.016  of  a  cubic  foot,  and 
as  tlie  cylinder  is  one  square  foot  in  sectional  area,  the 
piston  nmst  have  moved  up  a  distance  of  4.432  —  0.016 
=  4.416  feet. 

The  external  work  done  is  100  X  144  X  4.416  foot-jjounds. 
Dividing  this  by  778,  the  mechanical  equivalent  of  one  heat 
unit,  gives  as  a  result  81.9  B.  t.  u. 

The  heat  equivalent  of  the  external  work  is  represented 
by  Apu.  A  is  the  heat  equivalent  of  one  foot-pound  and 
is  equal  to  y^-g  ;  p  is  the  absolute  pressure  on  the  square 
foot ;  u  equals  the  change  in  volmne  in  passing  from  water 
to  steam. 

Subtracting  the  heat  equivalent  of  the  external  work  from 
the  total  latent  heat  gives  the  heat  equivalent  of  the  in- 
ternal work.  This  is  represented  l)y  the  Greek  letter  p 
(called  rho). 

In  tliis  case,  at  this  pressui-e,  p  amounts  to 

887.6-81.9=  805.7  B.t.u. 

This  heat  equivalent  of  the  internal  work  increases  as  the 
volume  of  a  pound  of  steam  increases. 

As  the  vohuue  occujiied  by  a  pound  of  steam  at  very  low 


PKUPEKTIES  OF  STEAM  A^s'^D  PERFECT  GASES  127 

pressures  is  large,  it  will  be  found  that  the  iuterual  latent 
heat  is  a  large  proportion  of  the  total  heat. 

Where  tliis  heat  goes  to,  may  be  illustrated  thus. 

All  substances  are  supposed  to  be  made  up  of  small 
particles  called  molecules. 

The  pound  of  water  occupying  0.016  of  a  cubic  foot  had 
a  certain  number  of  these  molecules.  The  number  remained 
the  same  in  the  pound  of  steam  which  filled  a  volume  of 
4.432  cubic  feet. 

The  relative  distance  between  these  molecules  has  been 
increased  275  times. 

Each  molecule  exerts  an  attraction  for  its  neighbor,  and 
as  tliis  attraction  has  been  overcome  thi-ough  space,  work 
has  been  done.  Tlus  work  has  required  an  equivalent 
expenditure  in  heat. 

Tliis  internal  Avork  is  often  called  dlsyregatloii  work. 


Total  heat 

A 

vapor 

..f  1 

lijuid          heat  of 

ization 

'J 

r 

heat  equivalent 
of  internal 

heat  equivalent 
of  external 

work 

work 

P 

Apu 

Volume  of  a  2^0 and  of  vuxture,  of  steam  ami  water : 
The  volume  of  a  pound  of  steam  is  s,  the  volume   of  a 

pound  of  water  is  0.016  of  a  cubic  foot. 

If  the  mixture  is  x  parts  steam  by  weight  the  volume   o 

of  the  pound  of  mixtm-e  is 

v  =  .r.s-+(l— a-)0.016 
v  =  x  (.s  —  0.016)  +  0.016 


128  PROPERTIES  OF  STEAJVI  AiiD  PERFECT  GASES 

Total  heat  of  a  pound  of  mixture  of  steam  and  water 
above  S^  : 

Before  any  water  can  be  made  into  steam  at  a  given 
pressure,  the  whole  of  the  water  must  first  he  heated  to  the 
temperature  corresponding  to  the  pressure.  Then  if  x  parts 
])y  weight  are  made  into  steam,  the  heat  x  r  nuist  he  added, 
making  the  total  heat  to  he  added  q  +  x  r. 

Total  heat  of  a  jpound  of  a  mixture  of  steam  and  water 
above  any  yiven  temperature. 

First  find  the  heat  of  the  pound  of  mixture  above  32° 
equal  to  5*  +  j"  r,  then  subtract  the  heat  of  the  liquid  at  the 
given  temperature. 

Superheated  steam  is  steam  of  a  liigher  temperature  than 
that  corresponding  to  saturated  steam  of  the  same  pressure. 

The  difPerence  of  teiuperature  is  the  number  of  degrees 
of  superheating. 

To  tell  whether  or  not  steam  is  superheated,  a  thermom- 
eter, a  steam  gage,  and  a  table  or  jjlot  giving  the  tempera- 
tui'es  of  saturated  steam  are  needed. 

Knoblauch,  Linde,  and  Klebe,  from  recent  experiments 
made  in  Munich,  have  determined  the  followdng  ecpiation 
for  sujierheated  steam  : 

pv  =  85.85  T—p  (1  +  0.n0O00f)7('.y>)      {  ^'^^"^y^^*^^^  —  0.0S328  [ 

A  much  more  simple  equation  giving  results  agreeing  with 
the  above  within  0.8  of  one  per  cent  is 

pv  =  85.85  T_  0.256^^ 

where  p  is  the  absolute  pressure  in  pounds  on  the  square 
foot,  and  v  is  the  volume  of  one  pound.  T  is  the  absolute 
temperature  of  the  superheated  steam  in  degrees  F. ;  this  is 
found  by  adding  459.5  to  the  temperature  of  the  steam  as 
given  by  the  thermometer. 

Having  the   temperature  and  pressure  as  known  terms, 


PROPERTIES  OF  STEAM  AXD  PERFECT  GASES 


129 


the  volume  niay  be  found,  or,  with  a  known  vokinie  and  a 
known  pressure,  the  temperature  may  lie  found. 

Specific  heat  of  superheated  steam  at  consta.nt  piressure 

It  was  formerly  assumed  that  this  speeilic  heat  of  super- 
heated steam  was  constant.  It  is  now  known  that  the 
specific  heat  increases  with  increase  in  pressure,  but  at  any 
constant  pressure  the  value  decreases  as  the  amount  of 
superheating  increases. 

The  mean  values  of  the  sjiecific  heat  for  different  pres- 
sures and  for  different  degrees  of  superheating,  as  given  by 
the  experimental  work  of  Thomas  &  Short,  are  quoted  in 
the  accompanying  table. 

Mean  Value  of  Specific  Heat  of  Superheated  Steam 
{Thomas  &  Short) 


Degrees  of 

Pressure,  pounds  per  square  inch,  absohite 

Superheat 
JFahr. 

6 

15 

30 

50 

100 

200 

20 

50 

100 

150 

200 
250 

0.536 
0.522 
0.503 
0.486 
0.471 
0.456 

0.547 
0.532 
0.512 
0.496 
0.480 
0.466 

0.558 
0,542 
0.524 
0.508 
0.494 
0.481 

0.571 
0.555 
0.537 
0.522 
0.509 
0.496 

0.593 
0.575 
0.557 
0.544 
0.533 
0.522 

0.621 
0.600 
0.581 
0.567 
0..556 
0..546 

Total  heat  of  a  pound  of  superheated  steam :  This  is 
evidently  equal  to  the  total  heat  of  a  pound  of  saturated 
steam  of  the  same  pressure,  ])his  the  average  value  of  the 
specific  heat  for  the  range  of  superheating  times  the  nmnber 
of  degrees  of  superheat. 

Using  the  letters  which  represent  the  different  values 

q  -\-  r  -\-  CpX  (degrees  superheat)  ; 

or 

X  +  Cp  X  (degrees  superheat). 


130  PROPERTIES  OP  STEAM  AND  PERFECT  GASES 

At  the  back  of  the  book  there  are  two  charts,  one  giving 
the  different  vahies  of  t,  q,  r,  X,  A  p  u,  p,  and  s  for  pres- 
sures from  0  to  10  pounds  absohite  and  the  other  giving 
vahies  of  the  same  terms  from  10  pounds  absohite  to  250 
pounds  absohite. 

These  curves,  which  are  drawn  to  represent  the  vahies 
given  in  Peabody's  Steam  Tables,  the  tables  in  general  use 
by  engineers,  will  serve  to  give  values  with  a  moderate  de- 
gree of  accuracy.  For  accurate  work  such  values  should  be 
taken  from  some  reliable  steam  table  which  gives  these 
values  for  each  degree  difference  of  temperature  or  for  each 
pound  increase  in  pressure. 

Tables  which  give  values  for  intervals  of  5  pounds,  and 
where  values  for  intermediate  points  must  be  obtained  by 
interpolation,  ai-e  fairly  accurate  at  high  pressures,  but  unre- 
liable at  low  ])i'essures  on  account  of  the  error  due  to  inter- 
])olation.  Even  tables  reading  to  one  pound  are  unreliable 
at  low  pressures  for  the  same  reason. 

If  either  Peabody's  Steam  Tables  or  the  Steam  Tables 
by  Marks  and  Davis  are  used,  all  low  jiressure  values 
should  be  taken  from  the  temperature  table  which  gives 
values  for  each  degree  from  32°,  The  pressure  correspond- 
ing to  each  temjjerature  is  given  also.  As  there  are 
seventy  sets  of  values  for  })ressiires  between  0  and  one  pound 
absolute,  sufficient  ac-curacy  can  be  obtained. 

The  charts  show  that  the  total  heat  and  the  heat  equiva- 
lent of  the  external  work  change  but  little  ;  that  the  tem- 
perature, the  specific  volume  of  steam,  and  the  heat 
equivalent  of  the  internal  work  (internal  latent  heat),  change 
rapidly  at  low  pressures  and  slowly  at  high  pressures. 

In  order  to  show  the  application  of  the  discussion  in  the 
preceding  images  a  few  examples  will  be  solved. 

Problem  (1).  How  much  heat  will  it  take  to  make  3 
pounds  of  water  at  00°  F.  into  wet  steam  at  150  pounds 
absolute  pressure  ?     The  steam  is  primed  2  j)er  cent. 


PROPERTIES  OF  STEAM  AXD  PERFECT  GASES  131 

If  the  wet  steam  contains  2  per  cent  moisture  there  must 
be  98  per  cent  dry  steam. 

In  solving  probleins  in  steam  where  use  is  made  of  the 
vakies  X,  q,  r,  s,  p,  A  p  i',  etc.,  it  must  be  remembered  that 
these  vahies  are  for  one  pound.  It  is  advisable  to  work  all 
problems  as  if  the  actual  weight  were  one  pound  and  to 
finally  multiply  the  result  by  the  actual  weight. 

The  heat  which  must  be  added  to  a  pound  of  water  at 
32°  in  order  to  make  this  into  wet  steam  at  this  pressure  is 
q  _|_  0.98r  where  q  and  /•  are  the  values  of  the  heat  of  the 
liquid,  and  the  total  latent  heat  at  150  pounds  absolute, 
respectively.  The  water  was  originally  at  60°.  The  heat 
of  the  liquid  of  water  at  60°  must  be  subtracted  from  this  to 
give  the  anu)unt  to  be  added  ])er  pound. 

(7  150  lbs.  ahs.    +  0.98r  150  1,,^    ^,,^    —  q  goo  p,)   X   S 

From  tile  chart  and  tlie  table  of  heat  of  the  licpiid  these 
values  are 

[330.  +  (0.98  X  863.0)  —  28.1]  X  3  =  3443. 

Problem  (2).  What  volume  will  the  3  pounds  of  wet 
steam  occupy  ? 

From  the  chart  it  appears  tliat  the  volume  of  one  pound 
of  dry  steam  at  150  ])ounds  absolute  pressure  is  3.0  cubic 
feet. 

The  volume  of  one  jiound  of  mixture  or  of  wet  steam  is 

V  =  0.98  (3.0  —  0.016)  +  0.016  =  2.940 
The  3  pounds  will  occu])y  a 

volume  =  3  y  =  8.820  cubi(t  feet. 

Problem  (3).  An  engine  is  supplied  with  steam  at  144 
pounds  absolute  pressure.  The  steam  contains  one  per  cent 
of  moisture. 

The  engine  uses  2,800  pounds  of  steam  per  hour  (all 
through  the  cylinders,  there  being  no  jackets). 


132  THERMAL  EFFICIENCY  OF  AN  ENGINE 

The  indicated  horse-power  is  200.  The  temj^erature  of 
the  exhaust  at  the  condenser  is  126°  F. 

The  air  pump  discharges  the  condensed  steam  l)ack  to 
the  boilers  through  a  primary  heater  on  the  exhaust  pi])e. 

The  temperature  of  the  feed-water  entering  the  boiler  is 
100°  F. 

Each  pound  of  coal  burned  under  the  l)oilers  gives  up 
14,500  B.  t.  u.,  9,900  of  which  are  taken  u])  by  the  boiler 
and  utilized  in  making  steam. 

What  is  the  number  of  pounds  of  coal  per  horse-power  as 
indicated  ? 

What  is  the  thermal  unit  consumption  of  the  engine  per 
horse-power  per  minute  ? 

_  2800 

\1  144  lbs.  abs.  +  0.  J  Jr  j_,4  „,j,  j,,,^  q  jOqo  fJ^TT 

gives  the  niimber  of  thermal  units  supplied  l)y  the  boiler  per 
1.  H.  P. 

Substituting  the  values  from  the  chart  or  tallies 
[326.7  +  (0.99  X  865.6)  —  68.0]  X  14  =  15619. 

Dividing  this  by  9900  gives  the  coal  per  I.  H.  P.  of  the 
engine  alone  as 

15619 

=  l.Oo  pounds. 

9900  ^ 

In  calculating  the  thermal  unit  consumption  of  the  engine 
it  is  customary  to  assume  that  the  condensed  steam  could  be 
returned  by  the  air-pump  to  the  boiler  at  the  same  tempera- 
ture as  that  of  the  exhaust  steam. 

The  thermal  unit  consumption  per  I.  H.  P.  per  minute  is 

V*/ 144  His.  abs.     I     ''•'^'''' 144  lbs.  abs.         'il260F.)    OOO  X  60   ~ 

(326.7  +  857.0  —  94.0)—  =  254.26 

Problem  (4).  Suppose  that  the  steam  supplied  to  the 
engine  was  of  144  pounds  absolute  pressure  and  400°  F.  in 
temperature ;    that    the   steam   consumption    per    hour  was 


CAKXOT  EXGIXE  133 

2,600   pounds,  and   that   the  I.  H.  P.  and  other  conditions 

were  the  same,  what  would  be  the  B.  t.  u.  per  I.  H.  P.  per 

minute  ? 

(  ")       2600 

I  X :«  u..  +  0.587  (400.0  -  355.29)  -  a  ,,,.  ,,  j-  ^^^-^^  = 

I  1192.3  +  26.24  —  94.0  I  -  =  243.65 
(  f  60  • 

The  specific,  lieat  of  superheated  steam  is  taken  from  the 
preceding  table  as  0.587. 

Should  the  engine  be  provided  with  steam  jackets  the 
weight  of  jacket  steam  per  H.  P.  per  minute  times  the  B.  t.  u. 
given  up  })y  the  condensation  of  one  pound  is  to  be  added  to 
the  B.  t.  u.  per  H.  P.  per  minute  through  the  cylinders. 

Problem  (5).  What  is  the  thermal  efficiency  of  the  en- 
gines in  (3)  and  (4)  as  previously  explained? 
33000 


7(8 


=  42.42  B.  t. 


*      42.42  42.42 

^f:_  =  0.1(37  -^^^^  =  0.174 

2.54.26  243. (w 

Carnot  engine.  It  is  found  in  tlie  preceding  problem 
that  the  thermal  efficiency  of  the  engines  is  low. 

One  might  be  led  to  think  that  the  steam  engine  was  not 
as  economical  as  it  might  be  made  to  be.  This  is  not  the 
case,  however.  Many  of  our  best  engines  when  compared 
in  thermal  unit  consumption  -wath  that  of  the  theoretically 
perfect  engine,  working  between  the  same  pressures  and 
temperatures,  give  70  per  cent  comparative  efficiency. 

The  theoretically  perfect  engine,  called  the  Carnot  engine, 
is  not  necessarily  one  with  100  per  cent  thermal  efficiency, 
but  one  in  whidi  there  are  no  losses  from  friction,  conduc- 
tion, radiation,  etc.  It  is  one  in  which  all  the  heat  supplied 
is  accounted  iav  by  the  sum  of  the  heat  A^thdrawn,  and  the 
lieat  transformed  into  work. 

Evidently  an  engine  to  have  100  per  cent  thermal  effi- 
ciency must  transform  all    the  heat  it  receives    into  work, 


134  CARXOT  EXGINE 

and  have  none  to  throw  away  oi-  be  Avithdrawn.  It  can  be 
shown  that  the  efficiency  of  such  a  theoretically  perfect  en- 
gine is  given  by  dividing  the  difference  of  teniperatui'e 
worked  through  in  the  cycle,  by  the  absolute  temperature  at 
wliich  heat  was  supplied  to  the  engine. 

A  Carnot  engine  working  through  the  same  temperature 
intervals  as  those  given  in  Problem  (3)  would  have  a  thermal 
efficiency  : 

355.29-126.   _  ^  ^81 
355.29  +  459.5 

Comparing  the  actual  with  that  of  the  Carnot : 

0.281 

The  thermal  unit  consumption  per  H.  P.  per  minute  for 
this  case  is  witli  tlic  Carnot  engine  : 

^^=151. 
0.281 

The  B.  t.  u.  consumed  per  H.  P.  per  minute  liy  the  actual 
engine  and  by  the  theoretical  liear  the  same  ratio  as  that  of 
the  thermal  efficiencies : 

^l^  =  o.r,9 

254.2() 

The  only  correct  way  to  quote  the  performance  of  an 
engine  is  by  its  thermal  efficiency  or  by  its  B.  t.  u.  consump- 
tion per  I.  H.  P.  per  minute. 

The  weight  of  steam  per  H.  P.  per  hour  does  not  mean 
anything  unless  one  knows  the  heat  in  that  steam  as  sup- 
plied to  the  engine  and  the  temperatiu-e  and  pi-essure  of  the 
exhaust. 

One  engine  may  develop  a  H.  P.  on  9  pounds  of  steam, 
the  steam  being  highly  superheated.  Another  engine  with 
perhaps  a  liigher  thermal  efficiency  than  the  first  may  use 
12  povmds  per  H.  P. 


NOX-COXDUCTIXG  EXGINE  135 

If  two  engines  work  under  exactly  the  same  conditions 
as  to  boiler  pressure,  steam,  and  vacuiun,  then  a  compari- 
son may  be  made  of  the  steam  consmnptions  per  H.  P.  per 
hour. 

In  the  Carnot  engine  it  is  supposed  that  the  same  charge 
of  working  substance,  air,  steam,  or  whatever  it  may  be,  is 
ailternately  heated  and  cooled  in  the  cylinder.  The  actual 
engine  has  a  new  supply  of  working  substance  brought  into 
the  cylinder  on  each  power  stroke. 

It  would  seem  better  to  compare  the  actual  engine  with  a 
perfect  engine  which  was  sunilaily  supplied.  By  a  perfect 
engine  is  meant  one  in  wliich  there  is  no  friction,  no  radia- 
tion, and  no  absoii)tion  or  conduction  of  heat  by  the  cylinder 
walls  ;  one  in  which  the  expansion  drops  the  pressure  down 
to  that  of  the  back  pressure.  Such  an  engine  is  called  a 
non-conducting  engine  or  an  engine  working  on  the  liankine 
cycle. 

Non-conducting  engine.  The  amount  of  heat  which  must 
be  added  to  a  pound  of  feed  water  at  the  boiler  to  make  it 
into  a  pound  of  steam  of  the  condition  as  suppUed  to  the 
engine,  assuming  that  the  feed  water  enters  the  boiler  at 
the  temperatiu'e  of  the  engine  exliaust,  is  q^  +  x^  i\  —  q^ ; 
where  qi  is  the  heat  of  the  liquid,  r^  the  total  latent  heat  or 
heat  of  vaporization  at  boiler  pressiu'e,  and  Xy  is  the  quality 
of  the  steam  made  by  the  boiler.  If  there  is  one  per  cent 
pruning  in  the  steam  then  Xy  =  0.99.  If  the  quaUty  of  the 
steam  after  an  adiabatic  expansion  from  cut-off  down  to  the 
back  pressure  is  a'g  the  heat  to  be  abstracted  during  the  ex- 
haust is  X2  ^2  where  ?*2  is  the  latent  heat  of  steam  at  the 
pressure  corresponding  to  the  exhaust. 

The  efficiency  of  any  engine  is  the  dilference  lietween  the 
heat  supplied  and  the  heat  exhausted  divided  by  the  heat 
supphed.     In  tliis  case  the  efficiency  becomes 
gi+^1^1— g2  — J^2^2  _  i__  ^2 '•2 


136  NON-COXDUCTING  ENGINE 

The  adiabatic  line  was  discussed  in  Chapter  I,  page  14. 
It  was  shown  that  for  a  reversible  line  the  entropy  remained 
constant.      This  fact  is  made  use  of  in  calculating  x^. 


/2.3026  1og.^  +  ^^)- 


where    T^  is  the  absolute  temperature  coi-responding  to  the 

temperature  of  the  steam  and  T^  that  of  the  feed  water.    The 

deiivation  of  the  formula  will  be  found  under  the  discussion 

of  the  temperature  entropy  diagram. 

Problem  (6).      What  would  be  the  thermal  efficiency  of 

a  non-conducting  engine  working  as  in  Problem   (3)   with 

steam  primed  one  per  cent  at  144  pounds  absolute  pressure 

and  with  exhaust  at  126°  F.  ?     What  would  be  the  number 

of  pounds  of  steam  per  H.  P.  per  hour  ?     What  would  be 

the  B.  t.  u.  consumption  per  H.  P.  per  minute  ? 

/  355.29+4.59.5  ,      0.99X865.(5X^126  +  459.5 

a:,  =  (  2.o02d  log.  —-. — ,    ,.-,  .    +  .,..  ,,,,    ,    ,.,..,    I X r-r^ 

^       \  ^    126. +459.5        3.d5.29  +  4o9.5/  1021 

x^  =  0.79 

The  efficiency    =1 ^.nQX102\. _  ^^ ^^ 

^  327.6  +   (0.99  X865.S)— 94  ' 

or  26  per  cent. 

The  foot-pounds  of  work  done  by  the  engine  per  pound 
of  wet  steam  supplied  is  778  {q^  +  .i\  )\  —  q^,  —  -f^^'i)  '■>  this 
being  the  difference  between  the  heat  supplied  and  the  heat 
exhausted  per  pound  or  the  heat  per  pound  transformed  into 
work  multiplied  by  778.  The  number  of  foot-pounds 
corresponding  to  a  H.  P.  for  one  hour  is  33,000  X  60.  The 
steam  per  H.  P.  per  hour  is  then 

33000  X  60 —  S  96 

778[327.6+(0.99X865.8)  — 94— (0.79X1021)]  ~ 

33000 


The  B.  t.  u.  consmiiption  per  H.  P.  per  minute  is 


778 
0.26  =  163.2.      The  engine  in  Problem  (3)  showed  an  actual 

efficiency  of  0.167.  This  is     '  _  ,    =  0.64,  or   64  per  cent  of 


TEMPERATUKE  ENTROPY  CHART  137 

that  of  the  non-conducting  engine,  and,  as  previously  shown, 
59  per  cent  of  that  of  a  Carnot  eugme. 


TEMPERATURE  ENTROPY  CHART  FOR  STEAM 

Under  the  discussion  of  entropy  it  was  pointed  out  that 
there  was  no  zero  of  entropy.  As  all  problems  involving 
quantities  of  heat,  internal  energy,  entropy,  etc.,  deal  vnth 
a  change  between  two  conditions,  tables  or  plots  of  such 
values  may  be  made  above  an  assmned  zero  ;  then  by  taking 
the  difference  of  the  readings  at  the  two  conditions,  each 
reading  being  above  the  assumed  zero,  the  correct  change 
between  the  two  conditions  may  be  obtained.  It  is  custom- 
ary to  take  32°  ¥.  as  the  assumed  zero.  On  the  plots  re}> 
resenting  the  })roperties  of  steam  the  values  of  q  and  \ 
are  so  reckoned.  The  temperatiu'e  entiopy  chart  is  similarly 
constructed. 

If  heat  is  added  to  a  pound  of  water  at  32°  F.  the  tem- 
perature of  the  water  rises  and  the  entropy  increases.  From 
what  has  been  said. in  a  preceding  chapter  it  is  e\4dent  that 
the  increase  in  the  entropy  of  the  liquid  between  32°  and 
any  high  temperature  must  be  foiuid  by  a  sunnnation  of  a 
large  number  of  terms.  If  the  sjjecific  heat  of  water  be  as- 
sumed as  constant  and  equal  to  luiity,  the  smnmation  of  an 
infinite  number  of  such  terms,  each  term  representing  the 
ratio  of  an  inhnitesimal  amount  of  added  heat  to  the  abso- 
lute temperature  at  wliich  it  was  added,  is  given  by  2.3026 

T 

log. »  where  T  is  the  absolute  temperature  at  the  upper 

491. .5 

condition  and  491.5  is    the  value  of  the  absolute  zero  corre- 
sponding to  32°  F. 

Referring  to  the  temperature  entropy  chart  it  will  be 
seen  that  entropy  is  measured  to  the  right  and  absolute 
temperatures  ai-e  measured  vertically.  If  now  the  entropy 
of  the  liquid  be  figm-ed  for  a  nmnber  of   temperatui-esj^nd 


138  TEMPERATUKE  ENTROPY  CHART 

the  values  so  figured  are  plotted,  a  line  marked  liquid  line 
will  be  obtained.  From  the  plot  the  entropy  of  the  liquid 
at  any  temperature  may  be  read  directly  : 

at  697.5°  absolute  the  entropy  of  the  liquid  is  0..S5 
at  800°  "        "         "        "    "       "      '^  0.49 

at  550°  "         "         "        "    "       "       "   0.11 

To  make  steam  at  a  given  pressure  from  water  at  32° 
the  water  is  first  heated  uj)  to  the  temperature  corresponding 
to  the  pressure  by  the  addition  of  the  heat  of  the  liquid  q. 
The  entropy  increases  by  an  amount  which  may  be  read 
from  the  liquid  line.  Next  the  heat  of  vajjorization  r  is 
added  and  the  water  gradually  passes  into  steam  at  the 
same    temperature.     The    increase    in    entropy  due  to   the 

addition  of  the  heat  of  vai)orization  is  — .      If  the  value  of 

T  T 

be  figured  for  each  pressure  and  laid  off  to  the  right  of  the 
li(|uid  line,  the  dry  steam  line  is  obtained.  If  instead  of 
vaporizing  the  entire  pound  of  water,  only  80  per  cent  of 
it  had  been  vaporized,  the  heat  added  at  constant  tempera- 
ture would  have  been  0.80  r  and  the  increase  in  entropy  due 

O.SO  r 
to  vaporization     ^^^  or  80  per  cent  of  the  value  between  the 

liquid  line  and  the  dry  steam  line.  The  horizontal  distance 
between  the  li(piid  fine  and  the  dry  steam  line  has  been 
divided  into  10  parts  marked  ./'  =  0.10,  x  =  0.20,  etc.,  and 
these  parts  each  subdivided  into  5  additional  parts. 

Illustration.  The  entropy  of  a  pound  of  dry  steam  at 
800°  absolute  temperature  is  read  from  the  chart  as  1.58. 
The  entropy  of  a  pound  of  dry  steam  at  550°  absolute  is  2.02. 
The  entropy  of  a  pound  of  mixture  of  steam  and  water 
which  is  80  per  cent  steam  by  weight  at  550°  absolute  is  1.64. 

Between  the  liquid  line  and  the  dry  steam  line  there  are 
four  curves  which  are  used  in  finding  the  absolute  tempera- 
ture corresponding  to  any  absolute  pressure. 


TEMPERATURE  ENTROPY  CHART  139 

The  absolute  temperature  of  steam 

at       2  pounds  absolute  pressure  appears  to  be  587. 5""' 
at       4  pounds         "  "  "        "     "   613.° 

at     10  pounds         "  "  "        "     "   654.° 

at  220  poimds         ''  "  "        "     "  850.° 

The  entropy  of  a  pound  of  mixture  of  steam  and  water  at 
50  pounds  absolute  pressure,  the  mixture  being  36  per  cent 
steam  by  weight,  is  read  on  the  chart  as  0.855. 

Beyond  the  dry  steam  line  are  lines  marked  250  pounds, 
200  pounds,  150  pounds,  etc.,  leading  upward  from  the  dry 
steam  line.  These  lines  give  the  entropy  of  superheated 
steam. 

Take  for  illustration  150  pounds  absolute.  This  line 
starts  from  the  dry  steam  line  at  818°,  the  absolute  temjiera- 
ture  of  saturated  steam  at  this  pressure  ;  as  heat  is  added  to 
the  dry  steam  and  the  pressure  kept  constant,  the  temperature 
increases  and  the  entropy  increases.  The  temperature  in- 
creases more  rapidly  than  the  entropy.  As  an  illustration, 
the  entropy  of  a  pound  of  steam  at  150  pounds  absolute 
})ressure,  superheated  100°  F.,  is  1.632. 

The  temperature  of  saturated  steam  at  150  pounds  is  818° 
al)solute. 

The  entropy  of  the  liquid  at  818°  absolute  is  0.513. 

The  entropy  of  a  pound  of  dry  steam  at  818°  is  1.565. 

The  increase  in  entropy  due  to  the  100°  superheat  is  .067. 

During  a  reversible  adiabatic  expansion  the  entropy  re- 
mains constant.  This  plot  is  a  great  help  in  solving  for  the 
iinal  condition  of  a  mixture  after  an  adiabatic  expansion. 
In  Problem  (6)  on  the  non-conducting  engine,  steam  at 
144  pounds  absolute  pressure  Avith  one  per  cent  priming  was 
expanded  adiabatically  to  126°  F.  or  585.5°  absolute.  It 
was  found  by  a  numerical  calculation  that  x.^  =  0.79.  This 
value  may  be  found  at  once  by  the  chart.  Follow  along  at 
the  temperature  level  corresponding  to  144  pounds  until  .r  = 


140  FLOW  OP  STEAM  THROUGH  AX  ORIFICE 

0.99  is  reached.  The  entropy  at  this  point  is  1.56.  Follow 
down  on  enti'opy  1.56  to  temperature  585.5  and  note  the 
value  oi  X  ;  x  is  found  to  he  0.79. 

Problem  (7).  Steam  at  100  pounds  alisolute  pressure, 
superheated  125°,  expands  adiahatieally  to  10  pounds  pres- 
siire  ahsolute.  What  per  cent  is  steam  at  the  end  of  the 
expansion  ?  At  what  pressure  is  the  steam  just  dry  ;  that  is 
with  no  moistui-e  and  with  no  superheat  ?  Follow  up  on 
the  100  ])ound  superheat  line  till  a  point  is  reached  125° 
ahove  the  temperature  at  which  this  line  starts  from  the  dry 
steam  line.  Read  the  entropy  at  this  upper  point  as  1.68. 
Follow  down  at  constant  entropy  till  the  dry  steam  line  is 
reached  at  a  temperature  of  725°  ahsolute.  At  this  tempera- 
ture level  the  pressure  is  found  from  the  pressure  curves  to 
he  38  pounds  ahsolute  ;  continue  on  entropy  line  1.68  down 
to  the  temperature  corresponding  to  10  pounds  and  note  x 
as  0.93. 

FLOW  OF  STEAM  THROUGH  AN  ORIFICE 

The  velocity  of  steam  at  lOO  to  150  pounds  pressure, 
issuing  from  an  orifice  into  the  air,  is  from  1,300  to  1,500 
feet  per  second.  The  weight  of  steam  discharged  through 
an  oritice  with  rounded  entrance,  having  150  pounds  abso- 
lute pressure  on  the  entrance  side,  will  be  the  same  in 
amount  for  any  back  pressure  from  90  jjounds  absolute 
down.  At  first  sight  this  does  not  seem  reasonable.  The 
pressure  drops  at  what  is  called  the  throat  or  the  smallest 
section  of  the  orifice  or  nozzle  to  0.6  the  absolute  entrance 
pressure,  provided  the  back  pressure  is  not  over  0.6  of  the 
entrance  pressvire.  Under  these  conditions,  as  the  throat 
pressure  and  the  velocity  at  the  throat  are  the  same,  the 
quantity  discharged  will  remain  constant  during  changes  in 
back  pi'essiire  from  0.6  of  the  boiler  pressure  down  to  zero. 
The  same  is  true  also  for  gases. 


DESIGN  OF  A  TURKIXE  NOZZLE  141 

Measurement   of  Dry  Steam,   by  the 
Flo IV  through  an  Orifice 

An  empirical  formula  known  as  Napier's  or  as  Rankine's 
gives  very  accurate  results. 

The  orifice  should  have  a  rounded  edge  at  entrance. 

W  =  the  weight  of  steam  flowing  per  second. 

P^  =  the  absolute  pressure  in  pounds  per  square  inch  on 
the  entrance  side. 

P2  =  the  absolute  pressure  in  pounds  per  square  inch  on 
the  exit  side. 

A  =  area  of  the  orifice  in  square  inches. 

Where  P^  is  e(pial  to  or  greater  than  |  P^ 

W  =  A^ 

70 

Where  P^  is  less  than  |  P., 

W  =  J  J  ^  —^ ::  [  ^  =  0.0292  J  (P  P.  — P.?)  ^ 

As  P2  approaches  Py  more  steam  goes  through  the 
orifice  than  this  formula  gives. 

This  second  formula  is  not  to  he  recommended  as  accu- 

p., 
rate  within    8   per   cent    when  — -  hears  the  ratio  0.85  or 

higher. 

Design  of  a  Tnrhhie  Nozzle  for  Complete  Expansion 

By  gi-adually  increasing  the  diameter  of  a  nozzle  beyond 
the  throat  or  smallest  section,  the  velocity  of  the  steam 
in  the  nozzle  may  be  increased  as  the  pressure  drojxs,  till  at 
the  end  of  the  nozzle  a  velocity  of  from  3,600  to  4,000  feet 
per  second  may  be  realized  if  the  back  pressure  is  low. 

By  complete  expansion  is  meant  a  drop  in  pressure  in  the 
nozzle  from  the  highest  to  the  lowest  pressure ;  that  is, 
there  is  no  drop  after  leaving  the  nozzle. 

The  method    commonly  used  in  calculating   a   nozzle   is 


142  DKSKiN  OF  A  TURBINE  NOZZLE 

given  ill  the  following  pages,  but  the  derivation  of  the  for- 
mulae used  is  omitted. 

Let  the  subscript  /  denote  eonditions  and  values  of  the 
liigh  pressure  steam  at  entrance  to  the  nozzle  ;  the  subscript 
/  similar  conditions  at  the  throat,  and  the  subscript  e  at  exit. 
H  1^  =  y^.  +  J•^  i\  for  saturated  steam. 
Hi  =  ill  "^  '■(•  ^~  ^ ';-  (degrees    of   superheat)    for    superheated 

steam, 
//j  =  y^  +  -Pf  i\  for  saturated  steam. 
Hf  =  qf  +  i\  +  6p     (degrees     superheat)     for     sui)erlieated 

steam. 

He  =  <Ie  +  *e  >'e- 

The  values  of  .r^  and  x^  are  read  from  the  temperature  en- 
tropy plot,  assuming  adiabatic  expansion  from  the  condition 
.'■^..  If  the  steam  is  superheated  to  start  with,  the  chart  is 
used  in  the  same  way  after  locating  the  starting  position. 
Call  V^  the  velocity  at  the  throat  in  feet  per  second  and 
Vg  the  velocity  at  the  exit. 

V,  =  224  ^{H-H,) 


The  area  of  the  throat  and  the  exit  sections  are  calculated 

lluis  :  The  volume  of  one  pound  of   steam  at  the  throat  is 

y;,=.r,(.sj  — 0.016) +  0.016 

where  Sf  is  the  volume  of  one  pound  of  dry  steam  at  the  throat 

pressure.      Should  the  steam  be  superheated  at  the  throat, 

the  volume  of  a  pound  would  be  calculated  by  the  formula 

given  in  the  earlier  part  of  tliis  chapter. 

Vf  X  weight  per  second 

=  area  of  throat  in  square  feet. 

In  finding  V^,  85  per  cent  of  //^  —  //^  was  used  l)ecause  a 
friction  loss  amounting  to  15  per  cent  of  H^  —  //^  was  as- 
smued  to  occur  in  the  nozzle.  The  friction  loss  up  to  the 
tlii'oat  is  small  and  is  not  considered  in  this  calculation.  A 
small  allowance  is  sometimes  ma<le  for  it,  however. 


DESIGN  OF  A  TURBINE  NOZZLE  143 

The  effect  of  this  friction  and  of  tlie  conduction  of  heat 

by  the  nozzle  is  to  make  the  steam  more  nearly  dry  at  exit 

than  itwould  have  been  after  an  expansion  at  constant  entropy. 

0.15  {Hi-  H,) 
The  increased  dryness  may  be  found  by  

This    added  to  x^  gives  Xj,  the   final  condition    leaving    the 

nozzle. 

v^  =  Xj  {s^  -  0.016)  +  0.016 

Vg  X  weight  per  second  .    . 
=  area  of  exit  in  square  feet. 

'  e 

Problem  (8).  A  de  Laval  turbine  of  350  H.  P.  rated 
capacity  is  supplied  mth  seven  nozzles.  The  pressure  of 
steam  at  entrance  is  200  pounds  absolute,  the  steam  being 
superheated  35°.  The  exit  pressure  is  2  pounds  absolute. 
Assume  the  friction  loss  in  the  nozzle  to  be  15  per  cent. 
Assmne  also  that  65  per  cent  of  the  kinetic  energy  of  the 
steam  is  utilized  by  the  wheel.  Find  steam  per  H.  P.  per 
liour  and  the  diameters  of  each  nozzle  at  exit  and  at  the 
throat. 

Refer  to  temperature  entropy  chart,  200  pounds  pres- 
sure, 35°  superheat.  The  entropy  is  1.57.  Follow  do\\ai 
on  1.57  until  the  temperatiu-e  corresponding  to  0.6  X  200  = 
120  poimds  pressure  is  reached.  Read  a-^  =  0.99.  Continue 
on  1.57  until  the  temperature  corresponding  to  2  poimds  is 
reached.      Read  x^  =  0.80. 

H^  =  354.3  +  843.5  +  (0.60  x  35)  =  1218.8 
H^  =  312.3  +  (0.99  X  876.9)  =  1180.4 
74  =  94.2  +  (0.80  X  1021.9)  =  911.7 
F,  =  224  v^  1218.8  - 1180.4  =  1393 
F,  =  224  v/O.85  (1218.8  —  911.7)  =  3618 
0.15  (1218.8  -  911.7)  ^  ^  ^^g 
1021.9 
x^=  x^-\-  0.045  =  0.80  +  0.045  =  0.845 


144  CALCULATING  THE  SIZE  OF  A  STEAM  MAIN 

The  kinetic    energy  per  pound  of    a  jet  issuing  vnih  a 

velocity  of  3,620  feet  per  second  is .      As   60  per 

•  '■  2  X  32.2  ^ 

cent  of  tliis  is  utilized,  the  energy  received  by  the  wheel  per 
second  per  pound  of  steam  is 

0.65  X  3620  X  3620  „ 

toot-povmds. 

64.4  ^ 

The  energy  needed  per  second  to  develop  350  H.  P.  is 
350  X  ''"^ 


m 

hence    the    numher    of    pounds    of    steam   which    must    be 
supjilied  per  second  is 

350  X  33000  X  (UA  -,   .kk 

=  1.455 

0.65  X  3620  X  3(>20  X  60 

The  steam  j^er  H.  P.  hour  is 

1.4.55  X  3600        -,  .  nc  n 

=  14.96  lbs. 

350 

The  steam  ])er  nozzle  per  second  is 

i:^  =  0.208  ll)s. 

7 

The  vohmie  of  a  pound  of  mixture  at  the  pressure  and 
the  condition  at  the  throat  is  0.99  (3.723  -  0.016)  +  0.016  = 
3.686  cul)ic  feet.  The  volume  of  a  pound  at  exit  is  0.845  X 
(173.1  -  0.016)  +  0.016  =  146.2  cubic  feet.  The  area  of 
the  tlu'oat  in  square  feet  is 

3.686  X  0.20s  A  -^Q  •     1        r        * 

;   or  O.oj  inches  diameter. 

1390 

The  area  of  the  nozzle  at  exit  in  scpiare  feet  is 

146.2  X  0.208  -,  00  .     ,        1- 

;  or  i.oo  inches  diameter. 

3620 

CALCULATING  THE  SIZE  OF  A  STEAM   MAIN 

The  indicator  when  apjjlied  to  the  steam  chest  as  ex- 
plained in  Part  II,  page  107,  sometimes  shows  that  the 
steam  pipe  is  not  large  enough  to  supply  the  engine. 


CALCULATING  THE  SIZE  OF  A  STEAM  MAIX  145 

If  the  pipe  is  furnishing  steam  to  a  slow  speed  engine, 
and  the  pipe  is  not  much  under  the  correct  size,  a  drum 
placed  in  the  steam  pipe  close  to  the  engine  may  remedy  the 
trouhle.  The  volume  of  this  drum  should  be  at  least  four 
times  the  volmne  of  the  cyhnder. 

If  the  pipe  supplying  a  high-speed  engine  is  too  small,  it 
will  have  to  be  changed  in  order  to  remedy  the  trouble. 

In  figuring  the  size  of  a  steam  pipe  or  steam  main  it  is 
customary  to  allow  6,000  feet  velocity  of  the  steam  per 
minute  if  the  pipe  is  short,  mth  l)ut  few  elbows.  If  the 
pipe  is  of  moderate  length,  5,000  feet  per  minute ;  4,000  is 
used  on  long  runs  where  there  are  many  elbows  and  bends. 

Knomng  the  weight  of  steam  to  be  carried  thi-ough  the 
\n\)e  ])er  minute,  and  knowing  also  the  loicest  ^;re.s.sv^re  at 
which  the  plant  ^^'ill  ever  work,  the  volume  of  the  steam  can 
l>e  figured.  This  volume  divided  by  the  allowable  velocity 
will  give  the  area  of  the  pipe  needed. 

Example :  300  pounds  of  steam  per  minute  are  to  be  car- 
ried through  the  pipe.  The  highest  ])ressure  at  which  the 
plant  runs  is  125  pounds  absolute.  The  lowest,  100  pounds 
absolute. 

From  the  cliart  it  is  found  that  the  volume  of  one  pomid 
of  steam  at  100  pounds  pressure  is  4.4  cubic  feet. 

^•^  ^  '^^^  =  0.264  sq.  ft.  =  38.01  sq.  in. 
5000  ^  ^ 

This  area  corresponds  to  6.96  inches  diameter. 
For  the  higher  pressure  an  area  of 

— =  0.216  sq.  ft.  is  needed 

5000  ^ 

If  the  pipe  has  this  area  the  velocity  of  steam  through 
the  pipe  at  the  loAver  pressure  will  be 


f 


^  X  5000  =  6100  feet  per  minute. 


146  PERFECT  GASES 

PERFECT   GASES 

The  characteristic  equation  of  a  perfect  gas  or  the  equa- 
tion giving  the  relation  between  the  absolute  pressure,  the 
volume  and  the  absolute  temperature  is 

T      T,      r. 

This  relation  was  determined  experimentally. 

The  volume  of  a  pound  of  air  at  atmospheric  pressure 
and  at  freezing  jDoint  has  been  determined  experunentally  to 
be  12.39  cubic  feet.     That  of  hydrogen,  178.2  cubic  feet. 

Atmospheric  pressure  is  14.7  pounds  on  the  square  inch, 
ov  2116.3  pounds  on  the  square  foot,  equivalent  to  29.92 
inches  of  mercury  or  760  mm.  of  mercury.  The  tempera- 
ture T  is  absolute  ;  as  has  been  stated,  this  is  found  by 
adding  459.5  to  the  reading  of  a  Fahrenheit  thermometer. 

A  few  exanqjles  will  best  illustrate  how  use  is  to  be  made 
of  this  equation. 

(1).  Wliat  will  be  the  volume  of  one  pound  of  air  at  100 
pounds  absolute  pressure  and  at  139.3°  F.  ? 
14.7  X  12.39  _      ioo  X  ;; 
491. .5  459.5  +  139.3 

V  =  2.22  cu.  ft. 

(2).  What  will  be  the  weight  of  a  cubic  foot  of  air  at 
this  pressure  and  temperature  ? 

-=—  =0.45  lbs. 
V       2.22 

(3).  An  air  compressor  draws  in  100  cubic  feet  of  free 

air  per  minute  at  14.6  pounds  pressure    (absolute)   and  at 

60°  F.     The  air  is  compressed  to   200  pounds  absolute  and 

leaves  at  120°  F.    What  is  the  volume  of  the  air  discharged  ? 

■       14.6  X  100  _     200  X  U 

459.5  +  60  ~  459.5  +  120 

V  =  8.14  cu.  ft. 

(4).  A  balloon  of  10.000  cubic  feet  ca])acity,  weighing 
together  with  car,  sand  bags,  etc.,   550  pounds,  has  9,000 


PERFECT  GASES  147 

cubic  feet  of  hydrogen  run  into  it  at  80°  F.  and  at  30.2 
inches  of  mercuiy  pressure,  this  being  the  temperature  and 
the  pressure  of  the  surrounding  air.  Find  the  weight  of 
gas  run  in  ;  the  pull  on  the  rope  holding  the  balloon  to  the 
gi-ound,  and  the  amount  the  balloon  would  have  to  be  light- 
ened in  order  for  it  to  reach  a  height  where  the  barometer 
reads  20  inches  and  the  temperature  is  32°  F.  ^Hiat  would 
be  the  pressure  of  the  gas  on  the  inside  of  the  balloon  at  the 
upper  level,  assuming  that  no  gas  escapes  ? 

The  lifting  force  is  the  ditference  between  the  weight  of 
the  air  displaced  by  the  hydrogen  and  the  weight  of  hydro- 
gen run  in. 

Call  Vfj  the  volume  of  one  pound  of  hydrogen  at  the 
])ressure  and  temperature  at  the  gi'ound,  and  J^  ^  that  of  a 
})ound  of  air  at  the  same  place. 


29.92  X  12.39 

491.5          " 

30.2  X   V^ 
539.5 

F.1  =  13.45  cu.  ft, 

29.92  X  17S.2 
491.5          ~ 

30.2  X   ^H 
539.5 

r,j  -=  193.2  cu.  ft. 

9000          9000 

=  (]{■/,)  —  46 

.() 

=  622.4  lbs. 

13.45         193.2 

622.4  —  550  =  72.4  pounds  pull  needed  to  bold  the 
V)alloon  to  the  groimd. 

As  the  balloon  rises  the  hydrogen  expands  and  fills  the 
balloon  ;  and  as  the  balloon  continues  to  rise,  the  hydrogen 
if  not  allowed  to  escape  would  produce  a  jiressure  tending  to 
rupture  the  balloon. 

The  weight  of  air  displaced  by  the  balloon  at  the  upper 
level  is  calculated  thus  : 

29.92  X  12.39       20  X   V\ 


491.5  491.5 


VI        18.52  cu.  ft. 


The  10,000  cid)ic  feet  of  air  displaced  weigh 

10000  roQ  -  11 

■ — —  =  539.;)  lbs. 
18.52 


148  ISOTHERMAL  LIXE 

As  no  hydrogen  has  escaped,  according-  to  the  assumption, 
its  weight  is  46.6  pounds,  as  found  previously. 

539.5  —  46.6  =  492.9 

550  —  492.9  =  57.1  Ihs.,  the  weight  of  sand  wliich  must 
be  thrown  ovit  in  order  to  reach  this  level. 

The  pressure  P  inside  of  the  balloon  at  the  upper  level  is 

30.2  X  9000        P  X  10000  „        ^ .  „   .     , 
=  ;          P  =  24.7  inches. 

539.5  491.5 

The  outside  air  pressure  is  20  inches,  so  the  excess  pres- 
sure inside  the  balloon  is  4.7  inches  of  mercury  or  2.35 
pounds  per  square  inch  approximately. 

Measureriient  of  air  hy  the  Jioir  through  an,  orifice  : 

Experiments  have  shown  that  the  following  empirical  for- 
mula gives  quite  accurate  results  for  orifices  up  to  one  inch 
in  diameter. 

The  orifice  should  ])e  made  with  a  rounded  entrance,  the 
radius  of  the  cvirve  being  equal  to  the  diameter  of  the  orifice, 
and  the  length  of  the  straight  part  of  the  orifice  should  be 
equal  to  the  diameter. 

Whei-e  the  pressui-e  on  the  entrance  side  of  the  orifice  is 
greater  than  twice  the  pressure  on  the  exit  side : 

P 

w  =  0.530  ^=  « 

y/T 

where  w  is  the  weight  of  air  per  second.  P  is  the  absolute 
pressure  on  the  square  inch  on  the  entrance  side.  T  is  the 
absolute  temperature  of  the  air  on  the  entrance  side,  a  is 
the  area  of  the  orifice  in  square  inches. 

Isothermal  line.  The  equation  for  an  isothermal  exjian- 
sion  or  compression  of  a  perfect  gas  is  Pi^  =  P^  'i;^,  or  the 
product  of  the  absokite  pressure  and  the  volume  is  a  constant. 
The  work  required  for  an  isothermal  conqjression,  or  devel- 
oped by  an  isothermal  expansion  of  a  gas  is 

Tr=  144  Pj  v^  X  2.3026  log.  ^ 

Pi 


ADIABATIC  LIXE  149 

where  W  is  in  foot-pounds.  J^j  is  the  absohite  pressure 
on  the  square  inch  at  the  beginning  of  compression  or  at 
the  end  of  expansion  ;  i\  is  the  vohmie  in  cubic  feet  at  this 
])ressm'e.  I^^  i^  tlie  absolute  pressure  on  the  square  inch  at 
the  end  of  an  isothermal  compression  or  at  the  beginning  of 
an  isothermal  expansion.  The  heat  which  must  be  ab- 
stracted   during  an  isothermal  comjiression   or  added  dvu'ing 

W 
an  isothermal  expansion  is  — . 

778 

Adlabatic  Hue.  The  equation  in  terms  of  pressure  and 
volmiie  representing  an  adiabatic  expansion  or  compression 
of  a  perfect  gas  is 

p   ,.  1.405    ^    p       ,,  1.405 
X     c  -^   1    '  1 

The  temperature  along  an  adiabatic  change  may  be  cal- 
culated by  combining  this  equation  with  the  characteristic 
equation  for  gases 

P  V        P^   v^ 
T     ~      T^ 
The  work  done  by  an  adiabatic  expansion  of  a  perfect 
gas  or  required  for  an  adiabatic  conqiression  is 

0.40.5  L  Wv,  /       J 

where  TT^  is  in  foot-pounds.  -P^  is  the  absolute  pressure  on 
the  square  inch  at  the  beginning  of  expansion  or  at  the  end 
or  compression ;  xi  ^  is  the  vohune  at  this  pressure,  -v  „  is 
the  volmne  after  the  expansion  or  at  the  beginning  of 
compression.     The  volumes  are  measured  in  cubic  feet. 

Tliis    value    —  will    always    come    out    less   th-an    unity. 

Suppose  for  illustration  —  =  0.3.     This  is  to  be  raised  to  the 

^2 
0.405    power.     The    logarithm    of     0.3    is    9.47712  —  10. 

Write  this  999.47712  —  1000  and  multiply  by  0.405  thus: 

(999.47712  —  1000)  x  0.405  =  (404.78823  —  405.)  or 

9.78823  -  10 

The  munber  corresponding  to  this  log.  is  0.G141. 


150  COMPRESSING  AIR 

COMPRESSING  AIR 

The  niininmin  work  required  to  compress  air  and  to  de- 
liver it  at  the  tenijierature  of  tlie  intake  would  he  that 
needed  for  an  isothermal  compression 

P  v^   =  P^  v^^ 

For  such  a  compression  heat  nuist  l)e  ahstracted,  as  has 
been  shown. 

If  no  heat  was  abstracted  during  compression  the  com- 
pression becomes  adiabatic  and 

P  V  i-«^  =  P^  y/'-'O-' 

The  ordinary  compressor  is  water  jacketed  and  although 
attempts  are  made  to  get  an  isothermal  com])ression,  the 
actual  compression  is  neither  isothermal  nor  adiabatic,  but 
somewhere  between  these  two  lines.  For  the  best  com- 
pressors a  line  having  the  equation 

p   ,.1.2    _    p^     ,,^1.2 

represents  the  compression.  The  compression  in  the  aver- 
age compressor  is  more  nearly  represented  by  a  Une  having 

the  equation 

p  ^,l.^  =  p     „  1.3 
J    (  ^  1   '  1 

The  H.  P.  required  at  the  compression  cylinders  of 
a  two-stage  compressor  to  compress  a  certain  number  of 
cubic  feet  of  free  air  (that  is,  cubic  feet  of  air  as  taken  from 
the  room)  per  minute,  from  the  pressure  at  the  eml  of  the 
suction  stroke  to  the  delivery  pressure  along  a  line  having 
the  equation 

P  v^"^  =  a  constant,  is 

144  X  2  X  Ps  y  X  1.3  {     /J^a\   'd_il 


(t) 


33000  X  0.90  X  0.3     ;     \p 
which  reduces  to 


0.0422  7^,  r  j  (^g)      -  1 1  =  H. 


COMPRESSIXG  AIR  151 

where  P^  is  the  ahsolute  pressure  per  s(piare  inch  at  end  of 
the  suction  stroke,  and  P^  is  the  ahsohite  dehvery  pressure  ; 
and  V  is  the  cubic  feet  of  free  air. 

For  a  tlu'ee-stage  comjjressor  this  fonuula  becomes 

0.0633  P-r\("\      -  1      =  H.  P. 

The  air  at  entrance  to  a  compressor  is  shghtly  rarefied, 
thus  making  P^  less  than  atmospheric  pressure,  and  the 
vohime  displaced  by  the  piston  of  the  compressor  has  to  be 
gi'eater  than  the  free  aii*  on  this  account  and  also  on  account 
of  the  clearance.  The  ratio  of  the  volume  of  free  air  per 
minute  to  the  piston  displacement  is  called  the  displacement 
efficiency.  For  the  very  best  com])ressors  with  mechan- 
ically operated  valves  this  is  approximately  95  per  cent. 
In  the  expression  just  given  for  calculating  H.  P..  a  value 
of  90  has  been  used  for  the  displacement  efficiency  as 
tliis  is  more  nearly  correct  for  the  ordinary  compressor. 

BE  A 


Fig.  58 

The  water  jackets  of  a  compressor  are  not  very  efficient 
in  a])stracting  the  heat  of  compression.  By  dividing  the 
(•()m])ression  up  between  two  or  more  cylinders  or  by  com- 
])ressing  in  stages  it  is  possible  to  cool  the  air  between 
stages  down  to  its  original  temperature  l)y  ])assing  it  through 


152  COMPRESSING  AIR 

inter-coolers  placed  Ijetvveen  the  compressor  cylinders.  This 
greatly  reduces  the  work  of  compression  as  is  shown  by  the 
illustration,  Fig.  58. 

The  vertical  line  represents  the  cylinder  head.  H  A  rep- 
resents the  entire  compression  as  taking  place  in  one  cylinder 
along  a  line  P  o  ^'^  =  a  constant.  The  dotted  line  H  B  rej> 
resents  an  isothermal  compression.  Air  compressed  along 
the  line  H  A  would  shrink  in  volume  from  A  to  B  as  it 
cooled  to  its  original  temperature  at  intake.  If  the  com- 
pression had  been  divided  into  two  stages  with  an  inter- 
cooler  between  the  two  cylinders  the  air  delivered  by  the 
first  stage  at  F  would  shrink  in  the  inter-cooler  to  the  volume 
at  G  before  entering  the  second  stage.  The  compression  in 
the  second  stage  is  along  a  line  G  E  of  equation  P  v  ^'^  = 
a  constant,  and  the  air  at  delivery  shrinks  from  E  to  B.  Evi- 
dently there  has  been  a  saving  of  work  equal  to  that  repre- 
sented by  the  area  F  G  E  A.  Against  this  saving  is  to  be 
charged  the  extra  mechanical  loss  due  to  the  friction  of  the 
second  cylinder.  For  a  two-stage  compression  the  absolute 
pressure  on  the  sqiiare  inch  Pp  is  equal  to  \  Pg  X  P^  the 
pressures  at  H  and  A  being  absolute.  For  a  three-stage 
compression  the  absolute   pi'essure  at  the  end  of  the   first 


stage  should  be  J  pi    x  P    ^^^^  ^^  the  end  of  the  second 


stage  the  pressure  should  be  Jp    x  P"    5  ^^  pressures  P^ 
and  P  ^  being  absolute. 

Problem  on  the  compressor.  1,000  cubic  feet  of  free  air 
per  minute  are  compressed  to  265.3  pounds  gage  pressure 
in  a  two-stage  compressor  which  is  steam  driven.  The  dis- 
placement efficiency  of  the  compressor  is  90  per  cent.  The 
pressure  in  the  first  cylinder  at  the  end  of  the  suction  stroke 
is  14.0  pounds  absolute,  or  0.7  pounds  below  the  atmos- 
phere. The  compression  is  along  a  line  P  v  ^  ^  =  a,  constant. 
Calculate  the  H.  P.  needed  at  the  compressor  cylinders,  and 
assuming  a  mechanical  efficiency  of  85  per  cent,  what  is  the 


PROBABLE  HORSE-POWER  OF  AN  ENGINE  IHS 

I.  H.  P.  needed  at  the  steam  cylinders  ?     Wliat  should  l>e 
the   pressure    at    the  end  of    the  coiupression  in    the    first 

stage  ? 

K  265.3  +  14.7 \  -1134         ) 
— )      ~   r  =  ^^^• 

244 

,— —  =  287  H.  P.  for  steam  cylinders.     Absolute  pressure 

0.85  ''  ^ 

at  end  of  first  stage  =  V^280  X  14  =  62.6 ;  or  47.9  pounds 

gage  jjressure. 

PROBABLE  HORSE-POWER  OF  AN  ENGINE 

The  method  of  finding  the  number  of  expansions  was 
explained  in  Chapter  I,  at  page  11.  As  far  as  the  power  de- 
veloped by  a  compound  or  triple  expansion  engine  is  con- 
cerned, the  total  number  of  expansions  worked  through  by 
the  steam  might  be  made  in  the  low  pressure  cyUnder.  By 
dividing  the  expansion  between  two  or  three  cylinders  the 
total  cylinder  condensation  is  reduced  and  a  better  rotative 
effect  is  obtained. 

The  expansion  line  of  an  indicator  card  does  not  vary 
nuich  from  a  rectangular  hyperlxda  having  the  equation 
P  V  =  a,  constant,  and  such  an  equation  is  commonly  as- 
sumed. 

The  entire  cycle  of  expansions  being  assumed  to  take 
place  in  the  low  pressure  cylinder,  the  M.  E.  P.  for  the  en- 
tire cycle  is  figaired  for  the  low,  and  this  M.  E.  P.  multiphed 
by  a  constant  between  0.7  and  0.9,  Avhich  makes  allowance  for 
the  losses  in  area  and  in  M.  E.  P.  due  to  the  rounding  of 
the  card  at  cut-off  and  at  release,  and  to  the  loss  due  to 
compression.  For  a  Corliss  valve  gear  these  losses  are  small 
and  the  multiplier  0.9  would  be  used.  For  a  plain  slide  valve 
a  nniltiplier  as  low  as  0.7  would  be  used. 

The  exi)ression  for  M.  E.  P.  is 

M.  E.  P.  =  -i  -1-  -i  X  2.3026  log.  n  —  I\ 
n        n  ° 


154  PROBABLE  HORSE-POWER  OF  AN  ENGINE 

where  Pj  is  the  ahsohite  boiler  pressure  in  pounds  on  the 
square  inch ;  P.,  the  back  pressure  on  the  square  inch  in 
pounds  absolute  ;  and  it  the  number  of  expansions.  One 
or  two  examples  will  show  the  application  of  this  formula. 

(1).  The  steamship  Nantucket  has  cylinders  28"  —  45" 
—  72"  X  54" ;  makes  94  revolutions  per  minute  ;  works 
against  a  back  pressure  of  2  pounds  absolute  ;  and  is  sup- 
plied with  steam  at  140  pounds  gage. 

The  cut-off  in  the  High  is  at  .70  stroke. 
"  "       "     "    Int.     "    "  .75      " 

u  a        u     u    Low    "     "  .75        " 

What  is  the  probable  H.  P.  ?  The  total  number  of  expan- 
sions is 

72X72      10       Q,,,. 
X  — ^  =  9.440 

2S  X  28        7 

M.  E.  P.  =  ^^  +  ^-^  X  2.3026  log.  9.446  -  2 
9.446      9.446  ^ 

=  16.377  +  36.777  -  2  =  51.15 

Considering    the  type  of    valve  gear  it  is  probable  that  a 

multiplier  of  0.77  would  be  about  right. 

0.77  X  51.15  =  39.38  as  the  probable  M.  E.  P. 

TT   -n         3.1416  X  72  X  72  X  39.38  X  94  X  2  X  .54       on^n 
H.  P.  = ■  =  3950 

4  X  33000  X  12 

(2).  An  engine  with  plain  slide  valve  gear  has  one  high, 
one  intermediate,  and  two  low  pressure  cylinders  ;  20"  — 
40" -2  (50")  X  60"  stroke; 

the  engine  runs  at  80  revs.  jDer  min. ; 

boiler  pressure  165.3  gage  ;  back  pressure  2  lbs.  abs.; 

as.sume  multiplier  for  gear  to  be  0.7  ; 

the  cut-off  is  at  ^  stroke  in  high  pressure  cylinder. 

-c,  .  2  X  .50  X  ,50  ^  2       or 

Expansions  =  n  = X  -  =  Zo. 

^  20  X  20  1 

Actual M. E.  P.=0.7(-W+ W X  2.3026 log.  25-2)  =  19.86 

-pj  p  _  3.1416  X  50  X  50  X  2  X  19.86  X  80  X  2  X  60  ^   ^gg^ 
4  X  33000  X  12 


CHAPTER  II 

METHOD  OF  CALCULATING  FROM  THE  INDICATOR  CARD 
FROM  A  STEAM  ENGINE,  THE  PER  CENT  OF  MIX- 
TURE ACCOUNTED  FOR  AS  STEAM  AT 
CUT-OFF  AND  AT  RELEASE 

Draw  on  the  indicator  card  a  line  at  each  end  of  the  card 
perpendicular  to  the  atmospheric  Hne.  Draw  a  Una  through 
the  point  of  cut-off  as  estimated  on  the  card  ;  also  a  line  just 
preceding  the  opening  of  the  exhaust  valve  as  shown  on  the 
card,  and  a  line  at  some  point  later  than  the  closure  of  the 
exhaust  valve  at  compression. 

The  pressures  at  cut-off',  release,  and  compression  are 
measured  above  the  atmospheric  line  and  the  pressure  of 
the  atmospliere  added. 

To  find  the  ]jer  cent  of  the  stroke  at  which  tliese  events 
occur,  a  scale  having  100  divisions  in  a  length  of  4  inches  is 
placed  diagonally  across  the  diagram  with  the  zero  on  the 
ordinate  at  one  end  of  the  card  and  the  100  on  the  ordinate 
at  the  other  end  of  the  card. 

The  percentage  at  cut-off,  at  release,  and  at  compression 
can  be  read  directly  from  this  scale. 

A  certain  amount  of  steam  is  brought  into  the  cylinder  at 
each  stroke,  and  the  same  amount  by  weight  is  exhausted 
per  stroke. 

The  weight  of  steam  used  per  stroke  can  be  found  by 
dividing  the  total  weight  of  the  condensed  steam  by  the 
total  strokes.  Call  tliis  weight  of  steam  per  sti'oke  through 
the  cylinder  M. 

There  is  a  certain  amount  of  steam  in  the  cylinder  at 
compression.  This  steam  at  compression  plus  the  amount 
brouglit  in  per  stroke  gives  the  total   weight  present  in   tlie 

155 


156        CALCULATING  PER  CEXT  OF  MIXTURE 

cylinder  up  to  cut-off  and  up  to  release.  This  is  called  the 
total  weight  o£  mixture. 

The  weight  of  steam  in  the  cylinder  at  compression  is 
found  by  assuming  that  the  space  between  the  piston  and 
the  head  of  the  cylinder,  including  port  passages,  is  filled 
with  dry  steam  of  the  absolute  pressure  at  compression. 

The  weight  at  compression  is  equal  to  the  (per  cent 
clearance  plus  the  per  cent  compression)  times  the  piston 
displacement  and  times  the  weight  of  a  cubic  foot  of  steam 
at  the  absolute  pressure  at  compression.  (The  weight  of  a 
cubic  foot  of  steam  is  the  reciprocal  of  the  volume  of  a 
pound.) 

Call  this  weight  at  compression  71/q. 

The   weight    of  mixture  in    the    cylinder    ])er    stroke  is 

The  volume  at  cut-off  is  equal  to  the  (})er  cent  clearance 
plus  the  per  cent  of  cut-off)  times  the  piston  displacement. 
Call  this  Fi. 

This  volume  is  filled  by  (M  +  J/y)  pounds  of  mixture  at 
the  absolute  j^ressure  of  steam  at  cut-off  as  obtained  from 
the  diagram. 

It  has  previously  been  shown  (page  127)  that  the  volume 
of  one  pound  of  mixture  is  V=x  (s — 0.016)  +  0.016 
where  x  is  the  per  cent  steam  by  weight. 

Hence  Fj,  the  volume  of  (M  +  J/p)  pounds,  nmst  equal 
Fi  =  {31  +  il/o)  X  (s  —  0.016)  +  {31  +  3Q  0.016.  The 
volume  .s  of  one  pound  of  steam  can  be  found  from  tables  or 
from  a  chart. 

X,  the  only  unknown  term,  is  obtained  by  solving  this 
equation. 

The  percentage  of  the  mixture  accounted  for  as  steam  at 
release  is  found  in  a  similar  way.  The  volume  V^  is  re- 
placed by  Vo,  the  volume  including  clearance  and  the  piston 
displacement  up  to  release. 

s  is  taken  at  the  absolute  pressure  at  release. 


CALCULATING  PER  CENT  OF  MIXTURE        157 

The  percentage  of  mixture  accounted  for  as  steam  at 
release  fre(juently  is  as  low  as  0.6. 

The  iiidicdtoi'  Jiij  itself  does  not  show  that  there  is  anij 
water  with  the  steam  in  the  cylinder.  If  the  steam  con- 
sumption of  an  engine  Is  figured  froTn  the  indicator  card, 
assuming  drij  steam  at  release  and  drij  steam  at  comjyres- 
sion,  (I  result  as  low  as  18  jiouiuls  rnaij  he  obtaiued  when 
the  actual  consuniption,  as  measured  hij  the  steam  con- 
densed in  the  condenser,  is  as  much  as  SO  pounds. 


CHAPTER  III 

DESIGN  OF  A  PLAIN  SLIDE  VALVE 

Valve  Setting  on  a  Plain  Slide  Valve  Engine  and  on  a 
Corliss  Engine 

Cards  taken  from  a  steam  engine  often  show  defects, 
which  may  l)e  due  to  an  improper  setting  of  the  valve,  as 
shown  in  Part  II,  or  to  a  poor  design  of  the  valve  gear. 

A  thorough  knowledge  of  the  plain  slide  valve  may  he 
hest  obtained  by  studying  some  one  of  the  graphical  methods 
used  in  designing  such  valves.  The  two  graphical  diagrams 
most  generally  used  are  the  Zeuner  and  the  Bilgram. 

In  nearly  all  stationary  engines  the  cross-head  is  con- 
nected to  the  crank  by  a  connecting  rod.  This  connecting 
rod  is  about  seven  times  the  length  of  the  crank.  In  some 
marine  engines  the  connecting  rod  is  only  three  and  one- 
half  times  the  length  of  the  crank. 

It  is  evident  that  when  the  crank  turns  from  0°  to  90°  on 
the  forward  stroke,  the  piston  moves  from  the  head  end 
center  towards  the  crank  end  a  distance  greater  than  one- 
half  its  entire  travel.  On  the  return  stroke,  starting  at  the 
crank  center,  the  piston  moves  through  less  than  half  its 
travel  during  the  first  90°  angular  motion  of  the  crank. 

If  instead  of  a  connecting  rod,  a  slotted  cross-head  had 
been  used  to  connect  the  cross-liead  to  the  crank  pin,  then 
the  same  angular  motion  of  the  crank,  from  either  center, 
Avould  make  the  same  displacement  of  the  cross-head  from 
either  end. 

If  the  crank  rotates  with  a  uniform  angular  velocity  the 
slotted  cross-head  is  said  to  move  in  harmonic  motion. 

The  smaller  the  ratio  of  the  length  of  the  connecting  rod 
to  that  of  the  crank  the  greater  is  the  variation  from  liar- 
monic  in  the  displacement  of  the  cross-head. 

158 


DESIUX   OF  A  PLAIN  SLIJJK  VALVP: 


159 


An  eccentric  and  an  eccentric  rod  are  equivalent  to  a 
crank  and  a  connecting  rod  ;  the  length  of  the  crank  being 
the  distance  f i-om  the  center  of  the  shaft  to  the  center  of  the 
eccentric,  called  the  eccentricity. 

An  eccentric  is  simply  a  crank  with  a  crank  pin  so  large 
that  it  takes  in  the  shaft.  The  diameter  of  the  eccentric 
has  nothing  to  do  with  the  travel  given  by  it ;  this  depends 
solely  on  the  eccentricity. 

The  eccentric  is  generally  set  from  95°  to  110°  ahead  of 
the  crank.  The  excess  over  90°  is  called  the  ungtdar 
advance. 

The  eccentric  rod  is  so  long  in  proportion  to  the  eccen- 
tricity of  the  eccentric  that  the  travel  of  the  valve  is  not 
affected  ap]jreciahly  by  the  slight  angular  movement  of  the 
eccentric  rod  and  it  is  customaiy  to  assume  that  the  valve 
moves  in  harmonic  motion. 


Fig.  59 


Tn  Fiff.  59  the  light  lines  show  the  crank  at  the  center 
and  the  eccentric  set  ^^'ith  an  angular  advance  d. 


160  ZEUNKK  DIAGRAM 

If  the  displacement  of  the  valve  is  measured  from  the 
middle  of  its  travel  it  is  evident  that  the  valve  is  displaced 
to  the  left  an  amount  a  o. 

The  maximum  displacement  to  the  left  will  he  a  b,  equal 
to  the  eccentricity,  and  will  occur  when  the  crank  is  at  the 
dotted  line  or  an  angle  d  hefore  the  90°  point. 

The  maximum  displacement  of  the  valve  to  the  right 
comes  at  a  crank  position  directly  opposite  to  this  dotted 
line.  The  valve  has  no  displacements  or  is  in  mid  position 
when  the  crank  is  at  the  position  shown  by  the  dash  lines  A 
at  position  making  an  angle  d  before  each  dead  point. 

Starting  at  the  crank  position  a  A  the  valve  is  in  mid 
position  and  has  no  displacement ;  as  the  crank  moves  in 
the  direction  of  the  arrow  the  valve  is  displaced  to  the  left, 
reaching  a  maxunmn  a  h  when  the  crank  is  at  the  dotted 
line ;  beyond  this  crank  position  the  displacements  of  the 
valve  gi'ow  less  till  at  the  crank  position  a  B  the  valve  is 
back  in  mid  position.  While  the  crank  is  turning  from  B 
to  A  the  valye  is  displaced  in  a  similar  manner  on  the  right- 
hand  side  of  mid  position. 

The  displacement  of  the  valve  for  the  ])osition  shown  by 
the  heavy  line  is  a  f. 

The  following  graphical  solution,  known  as  the  Zcitner 
Diagram,  will  give  the  disjilacement  of  the  valve  for  any 
crank  angle. 

The  actual  position  of  the  crank  and  eccentric  when  the 
engine  is  on  one  dead  center  is  shown  by  the  full  lines.  In 
this  graphical  solution  the  angle  d  is  laid  off  back  of  the  90° 
Une,  and  on  this  line  two  circles  are  drawn,  each  circle  be- 
ing made  of  a  diameter  equal  to  the  eccentricity  of  the 
eccentric. 

The  displacement  of  the  valve  from  mid  position  for  any 
crank  angle  is  equal  to  the  chord  cut  from  either  of  these 
circles  which  the  crank  position  may  intersect.  For  example, 
at  the  crank  position  O  8,  shown  by  the  dotted  line,  the  dis- 


ZEUNER  DIAGEAIVI 


161 


placement  of  the  valve  is  O  S  to  the  left  pf  the  mid  position. 
The  maximum  displacement  comes  at  a  crank  angle  Avhen 
the  chord  cut  is  of  maximum  length  or  at  angle  d  before  each 
of  the  90°  points. 

The  valve  has  no  displacement  or  is  in  mid  position  when 
there  is  no  chord  cut,  or  at  the  crank  position  O  INI  making 
an  angle  d  before  each  of  the  dead  points. 

These  positions  agree  with  those  as  found  in  the  previous 
discussion. 


M, 


d^^d- 


'U\ 


Fig.  60 


Starting  at  a  crank  position  0  M  (360°  —  d)  the  valve 
moves  from  mid  position  to  the  left,  reaching  a  maximmn 
distance  to  the  left  at  a  crank  angle  (90°  —  d)  ;  the  displace- 
ments gradually  grow  less  as  the  valve  comes  back  to  mid 
position,  which  is  reached  again  when  the  crank  is  at  O  M 


162  ZEUNER  DIAGRAM 

(180°  —  d).  From  this  point  on,  the  valve  is  similarly 
displaced  to  the  right  of  its  mid  position. 

A  section  through  a  plain  shde  valve  and  its  seat  is  given 
below.  It  is  seen  that  when  the  valve  is  in  mid  jjosition,  or 
in  the  center  of  its  travel,  the  outer  edge  of  each  end  of  the 
valve  overlaps  the  outer  edges  of  the  ports.  This  overlap  is 
called  the  outside  lap.  It  may  or  may  not  he  the  same  on 
the  two  ends  of  the  valve.  The  outer  edges  of  the  valve 
govern  the  admission  of  steam  and  the  cut-oif  of  steam. 

The  inner  edges  of  the  valve  overlap  the  inner  edges  of 
the  port  in  the  same  way.  This  distance  is  called  the  inside 
lap.  The  inside  edge  of  the  valve  governs  the  release  of 
steam  and  compression  of  steam. 


Fig.  61 

Considering  now  tlie  Zeuner  diagram  and  the  valve. 
When  the  crank  is  at  the  position  O  M  (360°  —  d)  the  valve 
is  in  mid  position,  as  shown  in  Fig.  61.  As  the  crank  reaches 
the  position  O  A  the  valve  is  displaced  to  the  left  a  distance 
O  E.  The  arc  O  E  is  drawn  with  a  radius  equal  to  the 
outside  lap  on  the  right-hand  end  of  the  valve.  At  this 
crank  position  the  outer  edge  of  the  valve  is  on  the  outer 
edge  of  the  port  and  admission  of  steam  is  ahout  to  begin ; 
see  Part  I,  Chapter  I,  page  6.  When  the  crank  gets  to 
the  dead  point,  the  displacement  of  the  valve  is  greater  than 
the  outside  lap  by  an  amount  /,  which  is  called  the  lead. 
This  lead  varies  from  0.01  of  an  inch  to  0.38  of  an  inch  in 
different  engines. 


ZEUNER  DIAGRAM  163 

When  the  crank  gets  to  an  angle  (90°  —  (/)  the  valve  is 
displaced  its  maximum  amount  to  the  left ;  the  outer  edge 
of  the  valve  is  now  to  the  left  of  the  outer  edge  of  the  port 
by  a  distance  equal  to  the  eccentricity  minus  the  outside  lap. 

The  valve  then  begins  to  move  back  to  its  mid  position 
and  at  a  crank  angle  O  C  the  outer  edge  of  the  valve  is  on 
the  outer  edge  of  the  port,  since  the  displacement  is  equal 
to  O  E,  the  outside  lap,  and  cut-oflE  occurs.  It  is  seen  that 
the  displacement  of  the  valve  is  the  same  at  cut-off  and  at 
admission  ;  at  admission  the  displacements  are  increasing 
and  at  cut-off  decreasing. 

After  cut-off,  the  steam  in  the  cylinder  expands  as  the 
valve  moves  to  mid  position  at  the  crank  angle  O  M  =  (180° 
—  d)  and  then.to  the  right  of  the  mid  position  till  the  crank 
angle  O  R  is  reached. 

At  the  crank  angle  O  R  the  valve  is  displaced  to  the  right 
of  the  mid  position  a  distance  O  Y,  which  is  equal  to  the  in- 
side lap  on  the  right-hand  end  of  the  valve.  {Note.  This  is 
drawn  out  of  proportion  on  the  diagram  in  order  to  avoid 
confusion.)  The  inner  edge  of  the  valve  is  now  on  the 
inner  edge  of  the  port  and  steam  is  al)out  to  escape  from  the 
cylinder  over  the  bridge  into  the  exhaust  port.  This  is  re- 
lease. Steam  is  exhausted  from  the  cylinder  from  the  crank 
])osition  O  R  to  the  crank  jjosition  O  K  when  the  inner 
Lulge  of  the  valve  is  again  on  the  inner  edge  of  the  port, 
giving  compression. 

The  dis])lacement  of  the  valve  at  release  and  at  compres- 
sion is  the  same  in  amount ;  the  displacements  at  release 
are  increasing  and  those  at  com])ression  decreasing. 

Consider  now  the  left-hand  end  of  the  valve,  which  con- 
trols the  distribution  of  steam  to  the  left-hand  end  of  the 
cylinder. 

P>vidently  the  valve  must  be  displaced  to  the  right  for  ad- 
mission and  cut-off  and  this  dis])la('ement  must  be  equal  in 
amount  to  the  outside  lap.  The  ai-c  o  z  is  drawn  with  a  ladius 


164  ZKUXKR  DIAGRAM 

equal  to  this  outside  lap.  Admission  conies  at  the  dead 
point.     There  is  then  no  lead.      Cut-off  comes  at  o  c. 

Release  and  compression  occur  when  the  valve  is  dis- 
placed to  the  left  o£  the  mid  position  an  amount  o  m  (drawn 
out  of  proportion)  equal  to  the  inside  lap.  This  brings 
release  at  o  r  and  compression  at  o  h. 

If  the  angular  advance  of  the  eccentric  is  decreased,  or 
the  angle  d  made  less,  admission,  cut-off,  release,  and  com- 
pression all  come  later  in  the  stroke,  as  was  shown  by 
Figs.  27  and  28,  Part  II,  page  103. 

If  the  angular  advance  is  increased,  or  the  angle  d  made 
larger,  all  the  events  come  sooner,  each  event  moving  ahead 
through  the  same  crank  angle. 

The  effect  on  the  laps,  both  inside  and  outside,  of  a  change 
in  the  length  of  the  valve  spindle,  was  pointed  out  in 
Part  II,  at  page  104.  The  diagram  makes  it  possible  to  trace 
out  the  effect  of  all  such  changes. 

Sujjpose  it  is  desired  to  increase  the  power  of  the  engine. 
The  cut-off  may  be  lengthened  by  decreasing  the  outside  lap 
and  the  release  delayed  by  increasing  the  inside  lap.  De- 
creasing the  outside  lap  would  make  admission  come  sooner 
and  increasing  the  inside  lap  would  make  compression  come 
earher.  To  prevent  these  from  coming  abnormally  early, 
the  angular  advance  of  the  eccentric  should  be  decreased. 

If  the  outside  lap  and  the  inside  lap  are  made  zero,  so 
that  the  length  of  each  foot  of  the  valve  is  just  equal  to  the 
width  of  the  steam  port,  compression  and  admission  will 
come  at  the  crank  position  0  M  and  cut-off  and  release  will 
come  at  the  crank  position  O  INI  opposite. 

If  the  inside  laps  O  M  and  O  Y  are  reduced,  the  release 
comes  sooner  and  the  comjoression  later.  If  these  are  made 
zero,  release  and  compression  come  180°  apart  at  O  M  and 
O  M.  If  it  is  desired  to  make  the  compression  come  still 
later,  the  inner  edge  of  the  valve  niay  be  cut  back  from  the 
inner    edge  of   the    port,  making  a  clearance.     Evidently, 


LAYIXG  OUT  A  PLAIN  SLIDE  VALVE  165 

when  a  valve  has  a  clearance  on  its  inner  edge,  to  bring  this 
edge  to  the  inner  edge  of  the  port  the  valve  must  he  dis- 
placed to  the  same  side  of  the  mid  position  that  it  was  for 
cut-off.  Tliis  means  that  the  arc  drawn  on  the  Zeuner  dia- 
gram to  represent  the  inside  clearance  would  he  on  the  same 
side  as  that  for  the  outside  lap. 

To  lay  oat  the  seat  for  a  value  :  The  width  of  the  steam 
ports  can  he  figured  by  assuming  a  velocity  of  steam  as  100 
feet  per  second,  and  the  length  of  the  port  as  about  0.8  the 
diameter  of  the  cylinder. 

Begin  at  the  end  of  the  valve  which  has  the  smaller  out- 
side lap.  Starting  at  the  outer  edge  of  the  port,  measure 
oft'  the  outside  lap.  This  outer  edge  of  the  valve  will  move 
to  the  right  and  to  the  left  a  distance  in  each  direction 
equal  to  the  eccentricity. 

To  allow  the  valve  to  over-travel  its  seat,  the  seat  is  de- 
pressed from  a  point  about  ^  inch  inside  of  the  extreme 
travel  out  to  the  ends  of  the  chest. 

The  travel  of  the  valve  in  the  other  direction  brings  the 
outer  edge  over  onto  the  bridge.  The  inner  edge  of  the 
bridge  should  be  about  -}  inch  beyond  this  j)oint.  The  inner 
edge  of  the  bridge  being  now  determined,  and  the  width  of 
the  steam  port  having  been  figured,  the  width  of  the  Inidge 
itself  is  known. 

To  find  the  width  of  the  exhaust  ^jort :  Lay  off  the  greater 
inside  lap  from  the  inner  edge  of  the  port  onto  the  bridge. 
It  may  happen  that  the  greater  inside  lap  does  not  come  on 
this  end  of  the  valve.  The  correct  lap  may  be  put  on  later 
after  the  width  of  the  exhaust  port  is  found.  Measure  from 
this  lap  towards  the  centei-  of  the  chest  a  distance  equal  to 
the  eccentricity,  then  add  the  width  of  the  steam,  port ; 
from  this  point,  which  is  the  inside  edge  of  the  bridge  of 
the  other  end,  lay  off  the  bridge  and  then  the  steam  port. 
Now  lay  out  the  laps. 


166  SETTING  A  PLAIN  SLIDE  VALVE 

SETTING  A  PLAIN  SLIDE  VALVE 

A  plain  slide  valve  is  almost  always  set  for  equal  lead. 
Tlie  amount  of  lead  and  the  direction  of  motion  of  the  en- 
gine depend  upon  the  position  of  the  eccentric.  The  equality 
of  the  lead  dej)ends  solely  upon  the  length  of  the  valve 
spindle. 

Put  the  engine  on  a  dead  center.  Remove  steam  chest 
cover.  Loosen  the  set  screws  holding  eccentric  to  shaft. 
Turn  the  eccentric  till  the  steam  port  on  one  end  is  open  its 
maximum  amount.  Caliper  this  distance  from  the  outer 
edge  of  the  port  to  outer  edge  of  the  valve.  Now  turn 
the  eccentric  until  the  maximum  port  opening  on  the  other 
end  is  reached.  Caliper  this  distance.  Lengthen  or  shorten 
the  valve  spindle  one-half  the  difference  between  these  two 
measurements  as  taken  hy  the  cali])ei'S,  lengthening  if  the 
head  end  o])ening  was  the  greater  and  shortening  if  the 
crank  end  was  the  greater. 

Turn  the  eccentric  in  the  direction  in  which  the  engine  is 
to,  run.  As  the  engine  is  on  the  center  the  valve  should 
move  so  as  to  open  the  port  on  that  end  of  the  cylinder  and 
when  the  port  has  opened  an  amount  corresponding  to  the 
lead  desired,  the  eccentric  should  he  set. 

By  setting  a  valve  hy  this  method  it  makes  no  difference 
whether  or  not  there  are  bell  crank  levers  or  rockers  be- 
tween the  eccentric  and  the  valve. 

SETTING  CORLISS  VALVES 

The  valves  of  a  Corliss  engine  may  be  set  quickest  by  the 
use  of  the  indicator.  If  there  is  reason  to  suspect  that  the 
valve  gear  is  very  badly  derangefl,  it  might  be  well  to 
see  that_  the  eccentric  has  a  small  angular  advance  and 
that  the  wrist  plate  swings  through  ecjual  angles  either 
side  of  the  vertical.  Sliould  these  angles  be  unequal,  the 
length  of  the  eccentric  rod  may  be  changed  till  e(|uality  is 
secured. 


SETTING  A  CORLISS  VALVE  GEAR  167 

The  engine  is  now  started  up  and  a  set  of  cards  taken. 
The  release  and  conijjression  are  adjusted  by  lengthening 
or  shortening  the  hnks  between  the  wrist  plate  and  the  ex- 
haust valves.  Lengthening  the  link  increases  the  exhaust 
lap  and  delays  release  and  hastens  compression  ;  shortening 
it  hastens  release  antl  delays  compression.  The  cut-ott'  is 
adjusted  last.  This  is  done  by  varying  the  length  of  the 
rods  from  the  governor  to  the  knock-off  tappets  and  may 
be  done  while  the  engine  is  running.  After  setting  the 
cut-off  the  engine  should  be  tested  with  the  governor  pushed 
up  against  the  top  collar  to  see  if  the  tappets  keep  the  claws 
from  engaging,  and  tested  also  with  the  governor  at  its 
lowest  position,  not  resting  on  the  starting  block,  to  see  if 
the  safety  tappets  prevent  the  claws  from  catching. 


EXPLANATION  OF  LOGARITHMS  AND  HOW  TO 
USE  THEM 

The  common  logarithm  of  a  numher  represents  the  power 
to  wliich  10  must  he  raised  to  equal  the  mimher.  Thus  the 
log.  100  =  2  hecause  10  must  he  raised  to  the  second  jiower 
to  equal  100.  The  log.  1000  =  3.  The  log.  10  =  1.  The 
log.  1  =  0.  Evidently  the  logaritlmi  of  a  numher  hetween 
1  and  10  will  he  hetween  0  and  1 ;  lietween  10  and  100 
will  he  hetween  1  and  2  ;  hetween  100  and  1000  hetween  2 
and  3.  The  logarithm  of  a  numher  less  than  1  will  he  con- 
sidered later. 

It  is  known  that  (r  X  (c^  =  a^  and  that  a''  -f-  ((^  =  (r. 
If  log.  3  =  .4771  and  log.  5  =  .6990  then  lO-*"'  =  3    and 

10-6990  =    5. 

5X3=  10*=^°°  X  10-^'"  =  lO-«»''"  +  -'"i  =  lOi-i'''' 
5 -=- 3  =  lO''''^"'^ lO'*"^  =  10-«»^-  ""1  =  l0-22i9 

To  multiply  two  numliers,  add  their  logarithms  and  this 
sum  is  the  logarithm  of  the  product ;  to  divide  one  numher 
hy  another,  suhtract  the  logarithms  of  the  numbers,  and  the 
result  is  the  logaritlun  of  the  answer. 

Example :  Multiply  5  X  4  X  20  X  3 ; 

log.  5  =  .6990 
log.  4  =  .6021 
log.  20  =  1.3010 
log.    3  =    .4771 

3.0792 

The  numher  corresponding  to  this  logarithm  is  1200. 
The  part  of  the  logarithm  to  the  left  of  the  decimal  point 
is  called  the  mantissa.     The  value  of  the  mantissa  deter- 

16S 


EXPLANATIOJq^  OF  LOGARITHMS  169 

mines  the  location  of  the  decimal  point  in  the  answer.    Thus 

log.  5  =     .6990 

log.  50  =  1.6990 
log.  500  =  2.6990 
log.  5000  =  3.6990 

It  is  seen  that  the  mantissa  is  one  unit  less  than  the  num- 
ber of  figures  to  the  left  of  the  decimal  point. 

The  part  of  the  logaritlun  to  the  right  of  the  decimal 
point  is  the  same  for  the  same  figures  irrespective  of  the 
location  of  the  decimal  point  in  the  number. 

Logarithm  of  a  Ninnher  Less   Than  1. 

log.  0.5  =  log.  Jq  =  log.  5  -  log.  10  =  .6990  —  1  = 

9.6990  —  10 

log.  0.05  =  log.  y|^  =  log.  5  —  log.  100  =  .6990  —  2  = 

8.6990  -  10 

log.  0.005  =  log.  yJg  0  =  log-  ^  -  log-  1000  =  .6990  —  3  = 

7.6990  -  10 

It  is    seen  that  the   logarithm  is  followed  by  —  10  and 

that  the  mantissa  is  9  if  the   left-hand  figure  of  the  number 

is  in  the  first  decimal  place,  8  if  in  the  second,  7  if  in  the 

tliird,  etc. 

_  ,       332.  X  4.13  X  (i9.5  X  0.95  X  0.00075 


njne . 

930 

log. 

332 

=    2.5211 

log- 

4.13 

=      .6160 

log. 

69.5 

=    1.8420 

• 

log. 

0.95 

=    9.9777- 

-10 

log. 

0.00075 

=     6.8751  - 

-10 

21.8319  - 

-20 

log. 

930 

=     2.9685 

18.8634  - 

■20 

170  EXPLANATION  OF  LOGARITHMS 

The  niimlier  corresponding  to  .8634  is  730;  18  —  20  is  the 
same  as  8  —  10  ;  this  indicates  that  the  left-hand  figure  is 
in  the  second  decimal  place,  or  0.0730  =  Ans. 

To  raise  a  numher  to  any  power,  multiply  the  log.  of  the 
number  by  the  exjjonent  of  the   power  and  the  result  is  the 
log.  of  the  answer. 
Examples :     (15)^ 

log.  15  =  1.1761 
2 
log.  Ans.  =  2.3522 
Ans.  =  225. 


(1.83)3 


log.  1.83  =  .2625 
3 


log.  Ayis.  =  .7875 
A71S.  =  6.13 

log.  1.83  =  .2625 ; 

multiply  by  ^  or  divide  by  4, 
log.  Ans.  =  .0656 
loff.  1.16  =  .0645 


11 
In  the  table  of  proportional  parts,  on  page   172,  at  the 
right  of  this  line  in  which  .0645  is  found,  11  corresponds 
to  3,  so  the  next  figure  is  3  and  the  answer  is  1.163. 

V0X)0373=  (0.00373)^ 

log.  0.00373  =  7.5717  —  10 

tliis  may  be  written  47.5717  —  50  ;  divide  by  5 ; 

log.  Ans.  =  9.5143  —  10 ; 
A71S.  =  0.3268 


TABLES 


172 


TABLES 


LOGARITHMS 


o 

Proportional  Parts 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

re 

1 

3 

3 

4 

5 

6 

7 

8  9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4 

8 

12 

17 

21 

25 

29 

33  37 

11 

04140453 

0492] 05 31 

0569  0607 

(1645 

0682 

0719 

0755 

4 

8 

11 

IS 

19 

23 

26 

30  34 

13 

0792,0828 

0864  0899 

0934!u969 

1004 

1038 

1072 

1106 

3 

7 

10 

14 

17 

21 

24 

28  31 

13 

1139:1173 

1206! 1239 

1271 

1303 

1335 

1367 

1399 

1430 

3 

6 

10 

13 

16 

19 

23 

26  29 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

3 

6 

9 

12 

15 

18 

21 

24  27 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

3 

6 

8 

11 

14 

17 

20 

22  2S 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

3 

5 

8 

11 

13 

16 

18 

21  24 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

2 

5 

7 

10 

12 

15 

17 

20  22 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

2 

5 

7 

9 

12 

14 

16 

19  21 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

2 

4 

7 

9 

11 

13 

16 

18  20 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

2 

4 

6 

8 

11 

13 

IS 

17  19 

31 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

2 

4 

6 

8 

10 

12 

14 

16  18 

33 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

2 

4 

6 

8 

10 

12 

14 

15  17 

33 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

2 

4 

6 

7 

9 

11 

13 

15  17 

34 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

2 

4 

5 

7 

9 

11 

12 

14  16 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

2 

3 

S 

7 

9 

10 

12 

14  15 

36 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

2 

3 

S 

7 

8 

10 

11 

13  IS 

37 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

3 

5 

6 

8 

9 

11 

13  14 

38 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

3 

5 

6 

8 

9 

11 

12  14 

39 

4624 

4639 

4654  4669 

4683 

4698 

4713 

4728 

4742 

4757 

3 

4 

6 

7 

9 

10 

12  13 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

3 

4 

6 

7 

9 

10 

11  13 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

3 

4 

6 

7 

8 

10 

11  12 

33 

5051 

5065 

5079  5092 

5105 

5119 

5132 

5145 

5159 

5172 

3 

4 

S 

7 

8 

9 

11  12 

33 

5185 

5198 

5211  5224 

5237 

5250 

5263 

5276 

5289 

5302 

3 

4 

5 

6 

8 

9 

10  12 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

3 

4 

5 

6 

8 

9 

10  11 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

2 

4 

5 

6 

7 

9 

10  11 

36 

5563 

5575 

5587 

5599 

5611 

5623  5635 

5647 

5658 

5670 

2 

4 

S 

6 

7 

8 

10  11 

37 

5682 

5694 

5705 

5717 

5729 

5740'5752|5763 

5775 

5786 

2 

3 

S 

6 

7 

8 

9  10 

38 

5798 

5809 

5821 

5S32 

5843 

5855 

5866  5877 

5888 

5899 

2 

3 

5 

6 

7 

8 

9  10 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977  5988 

5999 

6010 

2 

3 

4 

S 

7 

8 

9  10 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085  6096 

6107 

6117 

2 

3 

4 

5 

6 

8 

9  10 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 '6201 

6212 

6222 

2 

3 

4 

5 

6 

7 

8  9 

43 

6232 

6243 

6253;6263 

6274 

6284 

6294 '6304 

6314 

6325 

2 

3 

4 

5 

6 

7 

8  9 

43 

6335 

6345 

6355  6365 

6375 

6385 

6395  6405 

6415 

6425 

2 

3 

4 

5 

6 

7 

8  9 

44 

6435 

6444 

6454  6464 

6474 

6484 

6493  6503 

6513 

6522 

2 

3 

4 

5 

6 

7 

8  9 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590  6599 

6609 

6618 

2 

3 

4 

5 

6 

7 

8  9 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684  6693 

6702 

6712 

2 

3 

4 

5 

6 

7 

7  8 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776  6785 

6794 

6803 

2 

3 

4 

5 

5 

6 

7  8 

48  6812:6821 

6830 

6839 

6848 

6857 

6866'6875 

6884 

6893 

2 

3 

4 

4 

5 

6 

7  8 

49 

6902  6911 

6920 

6928 

6937 

6946 

6955^6964 

6972 

6981 

2 

3 

4 

4 

5 

6 

7  8 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042  7050 

7059 

7067 

2 

3 

3 

4 

S 

6 

7  8 

51 

7076 

7084 

7093 

7101  7110 

71187126  7135 

7143 

7152 

2 

3 

3 

4 

S 

6 

7  8 

53 

7160 

716S7177|71S5:7193 

72027210  7218 

7226 

7235 

2 

2 

3 

4 

5 

6 

7  7 

53 

7243 

725117259  7267'7275  728417292  7300!7308:7316 

2 

2 

^^ 

4 

5 

6 

6  7 

54 

7324  7332|7340j734Sl7356:7364|7372|7380l73S8|7396 

2 

2 

3 

4 

5 

6 

6  7 

TABLES 


173 


LOGARITHMS 


o 

Proportional  Parts 

0 

1        2 

3 

4 

5 

6 

7 

8 

9 

2; 

1 

3 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

j 
7412  7419 

742717435 

7443  7451 

1         1 
7459  7466  7474 

2 

2 

3 

4 

5 

5 

6 

7 

66 

7482 

7490  7497l75057513!7520!7528'7536i7543|7S51 

2 

2 

3 

4 

S 

5 

6 

7 

57 

7559,7566  75747582  75897597,7604  76127619;7627 

2 

2 

3 

4 

S 

5 

6 

7 

58 

7634 

7642,76497657  76647672 

76797686,7694:7701 

2 

3 

4 

4 

5 

6 

7 

59 

7709 

7716  7723  7731  7738  7745 

7752  7760 

7767  7774 

2 

3 

4 

4 

5 

6 

7 

60 

7782 

7789  7796  7803 ' 7810  7818 

7825  7832 

7839  7846 

2 

3 

4 

4 

5 

6 

6 

61    7853 

786017868  7875  7882  7889 

7896  7903 

79107917 

2 

3 

4 

4 

5 

6 

6 

63  ,7924  7931  7938  7945 

7952  7959 

7966  7973 

79807987 

2 

3 

3 

4 

5 

6 

6 

63  7993  8000  8007:8014 

80218028 

8035 

8041 

S048'8055 

2 

3 

3 

4 

5 

S 

6 

64 

8062,8069,8075  8082 

8089  8096 

8102 

8109 

8116 

8122 

2 

3 

3 

4 

5 

s 

6 

65 

8129  813618142  8149  8156'8162 

8169 

8176 

8182 

8189 

2 

3 

3 

4 

5 

5 

6 

66 

8195!S202  8209  8215  S222i8228 

8235 

8241 

8248 

8254 

2 

3 

3 

4 

5 

5 

6 

67 

8261; 8267  8274  8280  8287IS293 

8299 

8306 

8312 

8319 

2 

3 

3 

4 

5 

5 

6 

68 

8325 

S3^l!833S  8344  8351,8357 

8363 

8370 

8376 

8382 

2 

3 

3 

4 

4 

5 

6 

69 

8388 

8395 

8401 

8407 1 84 14 

8420 

8426 

8432 

8439 

8445 

2 

2 

3 

4 

4 

5 

6 

70 

8451 

8457 

8463 

8470  8476 

8482 

8488 

8494 

8500 

8506 

2 

2 

3 

4 

4 

5 

6 

71 

8513 

8519 

8525 

8531:8537 

8543 

8549 

8555 

8561 

8567 

2 

2 

3 

4 

4 

5 

5 

72 

8573 

8579 

8585  8591  8597 

8603 

8609 

8615 

8621 

8627 

2 

2 

3 

4 

4 

5 

5 

73 

8633 '8639 

8645  8651  865718663 

8669 

8675 

8681 

8686 

2 

2 

3 

4 

4 

5 

5 

74 

8692 j 8698 

8704  8710  8716 

8722 

8727 

8733 

8739 

8745 

2 

2 

3 

4 

4 

5 

5 

75" 

8751 

8756 

8762  8768  8774 

8779 

8785 

8791 

8797 

8802 

2 

2 

3 

3 

4 

5 

5 

76 

8808 

8814 

8820  8825  8831 

8837 

8842 

8848 

8854 

8859 

2 

2 

3 

3 

4 

5 

5 

77 

8865 

8871 

8876  8882  8887 

8893 

8899 

8904 

8910 

8915 

2 

2 

3 

3 

4 

4 

5 

78 

8921 

8927 

8932)8938  8943 

8949 

8954 

8960 

8965 

8971 

2 

2 

3 

3 

4 

4 

5 

79 

8976 

8982 

8987  8993  8998 

9004 

9009 

9015 

9020 

9025 

2 

2 

3 

3 

4 

4 

5 

80 

9031 

9036 

9042,9047  9053 

9058 

9063 

9069 

9074 

9079 

2 

2 

3 

3 

4 

4 

5 

81 

908519090 

9096  91019106  9112 

9117 

9122 

9128 

9133 

2 

2 

3 

3 

4 

4 

5 

83 

9138|9143  9149  9154  5159  9165  9170 

9175 

9180 

9186 

2 

2 

3 

3 

4 

4 

5 

83 

919l'9196  9201  9206  9212  9217  92229227 

9232 

9238 

2 

2 

3 

3 

4 

4 

5 

84 

9243  9248,9253  9258  9263,9269  9274;9279 

9284 

9289 

2 

2 

3 

3 

4 

4 

5 

85 

9294  9299 

93049309  9315  9320  9325 '9330 

9335 

9340 

1 

2 

2 

3 

3 

4 

4 

5 

86 

9345  9350 

9355  9360:9365  9370,9375  93So'9385 

9390    1 

2 

2 

3 

3 

4 

4 

5 

87  !9395i9400j9405  9410'9415i9420l942S  9430,9435 

94401  0 

2 

2 

3 

3 

4 

4 

88    9445  9450,9455  9460  946519469  9474  9479,9484 

9489:  0 

2 

2 

3 

3 

4 

4 

89   9494,949919504,9509  9513 

1          1          i          1 

9518  9523  9528  9533 

9538 

0 

2 

2 

3 

3 

4 

4 

90 

9542  9547  9552  9557  9562 

9566  95719576  9581 

9586 

0 

2 

2 

3 

3 

4 

4 

91 

9590  9595  9600  9605  9609 

9614  9619(9624  9628 

9633 

0 

2 

2 

3 

3 

4 

4 

93  i963S  964319647  9652  9657  9661,9666  9671i9675i9680i  0 

2 

2 

3 

3 

4 

4 

93 

9685  9689  9694  9699  9703]9708,9713  971719722 

9727 1  0 

2 

2 

3 

3 

4 

4 

94 

97319736|9741 

9745  9750  975419759  9763,9768 

9773:  0 

2 

2 

3 

3 

4 

4 

95 

9777 

9782  9786 

9791  9795 

9800  9805 ]9809  9814 

9818   0 

2 

2 

3 

3 

4 

4 

96 

9823 

9827  9832 

9836  9841 

9845  985019854  9859 

98631  0 

2 

2 

3 

3 

4 

4 

97 

9868;  9872 19877 

988119886  9890 1 9894  98*?l<5903 

9908   0 

2 

2 

3 

3 

4 

4 

98  '9912i9917l9921 

9926:9930  9934  9939  9943  9948 

9952    0 

2 

2 

3 

3 

4 

4 

99  ,9956  9961,9965 

9969  9974  9978  9983,9987  9991 

9996   0 

2 

2 

3 

3 

3 

4 

174 


TABLES 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

ADVANCING  BY   EIGHTHS 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

7.4613 

Diam. 

Area. 

Circum. 

1-64 

.00019 

.04909 

a  3-8 

4.4301 

6. 

28.274 

18.850 

1-32 

.00077 

.09818 

7-16 

4.6664 

7.6576 

1-8 

29.465 

19.242 

3-64 

.00173 

.14726 

1-2 

4.9087 

7.8540 

1-4 

30.680 

19.635 

1-16 

.00307 

.19635 

9-16 

5.1572 

8.0503 

3-8 

31.919 

20.028 

3-32 

.00690 

.29452 

5-8 

5.4119 

8.2467 

1-2 

33.183 

20.420 

1-8 

.01227 

.39270 

11-16 

5.6727 

8.4430 

5-8 

34.472 

20.813 

5-32 

.01917 

.49087 

3-4 

5.9396 

8.6394 

3-4 

35.785 

21.206 

3-16 

.02761 

.58905 

13-16 

6.2126 

8.8357 

7-8 

37.122 

21.598 

7-32 

.03758 

.68722 

7-8 

6.4918 

9.0321 

7. 

38.485 

21.991 

15-16 

6.7771 

9.2284 

1-8 

39.871 

22.384 

1-4 

.04909 

.78540 

3. 

7.0686 

9.4248 

1-4 

41.282 

22.776 

9-32 

.06213 

.88357 
.98175 

1-16 

7.3662 

9.6211 

3-8 

42.718 

23.169 

5-16 

.07670 

1-8 

7.6699 

9.8175 

1-2 

44.179 

23.562 

11-32 

.09281 
.11045 

1.0799 
1.1781 

3-16 

7.9798 

10.014 

5-8 

45.664 

23.955 

3-8 

1-4 

8.2958 

10.210 

3-4 

47.173 

24.347 

13-32 

7-16 
15-32 

1-2 
17-32 

.12962 
.15033 
.17257 

.19635 
.22166 

1.2763 
1.3744 
1.4726 

1.5708 
1.6690 

5-16 

3-8 

7-16 

1-2 

9-16 

5-8 

11-16 

3-4 

13-16 

7-8 

15-16 

4. 

8.6179 
8.9462 
9.2806 
9.6211 
9.9678 
10.321 
10.680 
11.045 
11.416 
11.793 
12.177 
12.566 

10.407 
10.603 
10.799 
10.996 
11.192 
11.388 
11.585 
11.781 
11.977 
12.174 
12.370 
12.566 

7-8 

8. 

1-8 
1-4 

3-8 

48.707 

50.265 
51.849 
53.456 
55.088 

24.740 

25.133 
25.525 
25.918 
26.311 

9-16 
19-32 

.24850 
.27688 

1.7671 
1.S653 

1-2 
5-8- 

56.745 
58.426 

26.704 
27.096 

5-8 
21-32 
11-16 
23-32 

.30680 
.33824 
.37122 
.40574 

1.9635 
2.0617 
2.1598 
2.2580 

3-4 
7-8 

9. 

1-8 

60.132 
61.862 

63.617 
65.397 

27.489 
27.882 

28.274 
28.667 

3-4 

.44179 

2.3562 

1-16 

12.962 

12.763 

1-4 

67.201 

29.060 

25-32 

.47937 

2.4544 

1-8 

13.364 

12.959 

3-8 

69.029 

29.452 

13-16 

.51849 

2.5525 

3-16 

13.772 

13.155 

1-2 

70.882 

29.845 

27-32 

.55914 

2.6507 

1-4 

14.186 

13.352 

5-8 

72.760 

30.2.S8 

7-8 

.60132 

2.7489 

5-16 

14.607 

13.548 

3-4 

74.662 

30.631 

29-32 

.64504 

2.8471 

3-8 

15.033 

13.744 

7-8 

76.589 

31.023 

15-16 

.69029 

2.9452 

7-16 

15.466 

13.941 

10. 

78.540 

31.416 

31-32 

.73708 

3.0434 

1-2 

15.904 

14.137 

1-8 

80.516 

31.809 

9-16 

16.349 

14.334 

1-4 

82.516 

32.201 

1. 

.7854 

3.1416 

5-8 

16.800 

14.530 

3-8 

84.541 

32.594 

1-16 

.8866 

3.3379 

11-16 

17.257 

14.726 

1-2 

86.590 

32.987 

1-8 

.9940 

3.5343 

3-4 

17.721 

14.923 

5-8 

88.664 

33.379 

3-16 

1.1075 

3.7306 

13-16 

18.190 

15.119 

3-4 

90.763 

33.772 

1-4 

1.2272  • 

3.9270 

7-8 

18.665 

15.315 

7-8 

92.886 

34-165 

5-16 

1.3530 

4.1233 

15-16 

19.147 

15.512 

3-8 

1.4849 

4.3197 

11. 

95.033 

34.558 

7-16 

1.6230 

4.5160 

5, 

19.635 

15.708 

1-8 

97.205 

34.950 

1-2 

1.7671 

4.7124 

1-16 

20.129 

15.904 

1-4 

99.402 

35.343 

9-16 

1.9175 

4.9087 

1-8 

20.629 

16.101 

3-8 

101.62 

35.736 

5-8 

2.0739 

5.1051 

3-16 

21.135 

16.297 

1-2 

103.87 

36.128 

11-16 

2.2365 

5.3014 

1-4 

21.648 

16.493 

5-8 

106.14 

36.521 

3-4 

2.4053 

5.4978 

5-16 

22.166 

16.690 

3-4 

108.43 

36.914 

13-16 

7-8 

15-16 

2.5802 
2.7612 
2.9483 

5.6941 
5.8905 
6.0868 

3-8 
7-16 

1-2 
9-16 

22.691 
23.221 
23.758 
24.301 

16.886 
17.082 
17.279 
17.475 

7-8 

12. 

1-8 

110.75 

113.10 
115.47 

37.306 

37.699 
38.092 

2. 

3.1416 

6.2832 

5-8 

24.850 

17.671 

1-4 

117.86 

38.485 

1-16 

3.3410 

6.4795 

11-16 

25.406 

17.S68 

3-8 

120.28 

38.877 

1-8 

3.5466 

6.6759 

3-4 

25.967 

18.064 

1-2 

122.72 

39.270 

3-16 

3.7583 

6.8722 

13-16 

26.535 

18.261 

5-8 

125.19 

39.663 

1-4 

3.9761 

7.0686 

7-8 

27.109 

18.457 

3-4 

127.68 

40.055 

5-16 

4.2000 

7.2649 

15-16 

1     27.688 

18.653 

7-8 

130.19 

40.448 

•TAHLES 


175 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  ,^^  to  99,  advancing  by  Tenths 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

0.0 
.1 
.2 
.3 

.4 

.007854 
.031416 
.070686 
.12566 

■  .31416 
.62832 
.94248 
1.2566 

5.0 
.1 
.2 
.3 
.4 

19.6350 
20.4282 
21.2372 
22.0618 
22.9022 

15.7080 
16.0221 
16.3363 
16.6504 
16.9646 

10.0 
.1 

.2 
.3 
.4 

78.5398 
80.1185 
81.7128 
83.3229 
84.9487 

31.4159 

31.7301 
32.0442 
32.3584 
32.6726 

.5 
.6 
.7 
.8 
.9 

.19635 

.28274 
.38485 
.50266 
.63617 

1.5708 
1.8850 
2.1991 
2.5133 
2.8274 

.5 
.6 

.7 
.8 
.9 

23.7583 
24.6301 
25.5176 
26.4208 
27.3397 

17.2788 
17.5929 
17.9071 
18.2212 
18.5354 

.5 
.6 

.7 
.8 
.9 

86.5901 
88.2473 
89.9202 
91.6088 
93.3132 

32.9867 
33.3009 
33.6150 
33.9292 
34.2434 

1.0 
.1 
.2 
.3 

A 

.7854 

.9503 

1.1310 

1.3273 

1.5394 

3.1416 
3.4558 
3.7699 
4.0841 
4.3982 

6.0 
.1 
.2 
.3 
.4 

28.2743 
29.2247 
30.1907 
31.1725 
32.1699 

18.8496 
19.1637 
19.4779 
19.7920 
20.1062 

11.0 
.1 
.2 
.3 
.4 

95.0332 
96.7689 
98.5203 
100.2875 
102.0703 

34.5575 
34.8717 
35.1858 
35.5000 
35.8142 

.5 
.6 

.7 
.8 
.9 

1.7671 
2.0106 
2.2698 
2.5447 
2.8353 

4.7124 
5.0265 
5.3407 
5.6549 
5.9690 

.5 
.6 

.7 
.8 
.9 

33.1831 
34.2119 
35.2565 
36.3168 
37.3928 

20.4204 
20.7345 
21.0487 
21.3628 
21.6770 

.5 
.6 
.7 
.8 
.9 

103.8689 
105.6832 
107.5132 
109.3588 
111.2202 

36.1283 
36.4425 
36.7566 
37.0708 
37.3850 

2.0 
.1 
.2 
!3 
.4 

3.1416 
3.4636 

3.8013 
4.1548 
4.5239 

6.2832 
6.5973 
6.9115 
7.2257 
7.5398 

7.0 
.1 

.2 

.3 
.4 

38.4845 
39.5919 
40.7150 
41.8539 
43.0084 

21.9911 
22.3053 
22.6195 
22.93.% 
23.2478 

12.0 
.1 
.2 
.3 
.4 

113.0973 
114.9901 
116.8987 
118.8229 
120.7628 

37.6991 

38.0133 
38.3274 
38.6416 
38.9557 

.5 
.6 
.7 
.8 
.9 

4.9087 
5.3093 
5.7256 
6.1575 
6.6052 

7.8540 
8.1681 
8.4823 
8.7965 
9.1106 

.5 
,6 
.7 
.8 
.9 

44.1786 
45.3646 
46.5663 
47.7836 
49.0167 

23.5619 
23.8761 
24.1903 
24.5044 
24.8186 

.5 
.6 
.7 
.8 
.9 

122.7185 
124.6898 
126.6769 
128.6796 
130.6981 

39.2699 
39.5841 
39.8982 
40.2124 
40.5265 

3.0 
.1 
.2 
.3 
.4 

7.0686 
7.5477 
8.0425 
8.5530 
9.0792 

9.4248 
9.7389 
10.0531 
10.3673 
10.6814 

8.0 
.1 
.2 
.3 
.4 

50.2655 
51.5300 
52.8102 
54.1061 
55.4177 

25.1327 
25.4469 
25.7611 
26.0752 
26.3894 

13.0 
.1 
.2 
.3 
.4 

132.7323 
134.7822 
136.8478 
138.9291 
141.0261 

40.8407 
41.1549 
41.4690 
41.7832 
42.0973 

.5 
.6 
.7 
.8 
.9 

9.6211 
10.1788 
10.7521 
11.3411 
11.9459 

10.9956 
11.3097 
11.6239 
11.9381 
12.2522 

.5 
.6 

.7 
.8 
.9 

56.7450 
58.0880 
59.4468 
60.8212 
62.2114 

26.7035 
27.0177 
27.3319 
27.6460 
27.9602 

.5 
.6 
.7 
.8 
.9 

143.1388 
145.2672 
147.4114 
149.5712 
151.7468 

42.4115 
42.7257 
42.0398 
43.3540 
43.6681 

4.0 
.1 
.2 
.3 
.4 

12.5664 
13.2025 
13.8544 
14.5220 
15.2053 

12.5664 
12.8805 
13.1947 
13.5088 
13.8230 

9.0 
.1 
.2 
.3 
.4 

63.6173 
65.0388 
66.4761 
67.9291 
69.3978 

28.2743 
28.5885 
28.9027 
29.2168 
29.5310 

14.0 
.1 
.2 
.3 
.4 

153.9380 
156.1450 
158.3677 
160.6061 
162.8602 

43.9823 
44.2965 
44.6106 
44.9248 
45.2389 

.5 
.6 
.7 
.8 
.9 

15.9043 
16.6190 
17.3494 
18.0956 
18.8574 

14.1372 
14.4513 
14.7655 
15.0796 
15.3938 

.5 
.6 
.7 
.8 
.9 

70.8822 
72.3823 
73.8981 
75.4296 
76.9769 

29.8451 
30.1593 
30.4734 
30.7876 
31.1018 

.5 
.6 

.7 
.8 
.9 

165.1.W0 
167.4155 
169.7167 
172.0336 
174.3662 

45.5531 
45.8673 
46.1814 
46.4956 
46.8097 

176 


TABLES 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  Jg  to  99,  advancing  by  Tentlis 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

15.0 
.1 
.2 
.3 
.4 

176.7146 
179.0786 
181.4584 
183.8539 
186.2650 

47.1239 
47.4380 
47.7522 
48.0664 
48.3805 

20.0 
.1 
.2 
.3 
.4 

314.1593 
317.3087 
320.4739 
323.6547 
326.8513 

62.8319 
63.1460 
63.4602 
63.7743 
64.0885 

25.0 
.1 
.2 
.3 
.4 

490.8739 
494.8087 
498.7592 
502.7255 
506.7075 

78.5398 
78.8540 
79.1681 
79.4823 
79.7965 

.5 
.6 
.7 
.8 
.9 

188.6919 
191.1345 
193.5928 
196.0668 
198.5565 

48.6947 
49.0088 
49.3230 
49.6372 
49.9513 

.5 
.6 
.7 
.8 
.9 

330.0636 
333.3916 
336.5353 
339.7947 
343.0698 

64.4026 
64.7168 
65.0310 
65.3451 
65.6593 

.5 
.6 

.7 
.8 
.9 

510.7052 
514.7185 
518.7476 
522.7924 
526.8529 

80.1106 
80.4248 
80.7389 
81.0531 
81.3672 

16.0 
.1 
.2 
.3 
.4 

201.0619 
203.5831 
206.1199 
208.6724 
211.2407 

50.2655 
50.5796 
50.8938 
51.2080 
51.5221 

21.0 
.1 
.2 
.3 
.4 

346.3606 
349.6671 
352.9894 
356.3273 
359.6809 

65.9734 
66.2876 
66.6018 
66.9159 
67.2301 

26.0 
.1 
.2 
.3 
.4 

530.9292 
535.0211 
539.1287 
543.2521 
547.3911 

81.6814 
81.9956 
82.3097 
82.6239 
82.9380 

.5 
.6 

.7 
.8 
.9 

213.8246 
216.4243 
219.0397 
221.6708 
224.3176 

51.8363 
52.1504 
52.4646 
52.7788 
53.0929 

.5 
.6 
.7 
.8 
.9 

363.0503 
366.4354 
369.8361 
373.2526 
376.6848 

67.5442 
67.8584 
68.1726 
68.4867 
68.8009 

.5 
.6 
.7 
.8 
.9 

551.5459 
555.7163 
559.9025 
564.1044 
568.3220 

83.2522 
83.5664 
S3. 8805 
84.1947 
84.5088 

17.0 
.1 
2 
'.3 
A 

226.9801 
229.6583 
232.3522 
235.0618 
237.7871 

53.4071 
53.7212 
54.0354 
54.3496 
54.6637 

22.0 
.1 
.2 
.3 
.4 

380.1327 
383.5963 
387.0756 
390.5707 
394.0814 

69.1150 
69.4292 
69.7434 
70.0575 
70.3717 

27.0 
.1 

'.3 
A 

572.5553 
576.8043 
581 .0690 
585.3494 
589.6455 

84.8230 
85.1372 
85.4513 
85.7655 
86.0796 

.5 
.6 

.7 
.8 
.9 

240.5282 
243.2849 
246.0574 
248.8456 
251.6494 

54.9779 
55.2920 
55.6062 
55.9203 
56.2345 

.5 
.6 
.7 
.8 
.9 

397.6078 
401.1500 
404.7078 
408.2814 
411.8707 

70.6858 
71.0000 
71.3142 
71.6283 
71.9425 

.5 
.6 
.7 
.8 
.9 

593.9574 
598.2849 
602.6282 
606.9871 
611.3618 

86.3938 
86.7080 
87.0221 
87.3363 
87.6504 

IS.O 
.1 
.2 
.3 
.4 

254.4690 
257.3043 
260.1553 
263.0220 
265.9044 

56.5486 
56.8628 
57.1770 
57.4911 
57.8053 

23.0 
.1 
.2 
.3 
.4 

415.4756 
419.0963 
422.7327 
426.3848 
430.0526 

72.2566 
72.5708 
72.8849 
73.1991 
73.5133 

28.0 
.1 
.2 
.3 
.4 

615.7522 
620.1582 
624.5800 
629.0175 
633.4707 

87.9646 

88.2788 
88.5929 
88.9071 
89.2212 

.5 
.6 

.7 
.8 
.9 

268.8025 
271.7164 
274.6459 
277.5911 
280.5521 

58.1195 
58.4336 
58.7478 
59.0619 
59.3761 

.5 
.6 
.7 
.8 
.9 

433.7361 
437.4354 
441.1503 
444.8809 
448.6273 

73.8274 
74.1416 
74.4557 
74.7699 
75.0841 

.5 
.6 

.7 
.8 
.9 

637.9397 
642.4243 
646.9246 
651.4407 
655.9724 

89.5354 
89.8495 
90.1637 
90.4779 
90.7920 

19.0 
.1 
.2 
.3 
.4 

283.5287 
286.5211 
289.5292 
292.5530 
295.5925 

59.6903 
60.0044 
60.3186 
60.6327 
60.9469 

24.0 
.1 

.2 
.3 
.4 

452.3893 
456.1671 
459.9606 
463.7698 
467.5947 

75.3982 
75.7124 
76.0265 
76.3407 
76.6549 

29.0 
.1 
.2 
.3 
.4 

660.5199 
665.0830 
669.6619 
674.2565 
678.8668 

91.1062 
91.4203 
91.7345 
92.0487 
92.3628 

.5 
.6 

.7 
.8 
.9 

293.6477 
301.7186 
304.8052 
307.9075 
311.0255 

61.2611 
61.5752 
61.8894 
62.2035 
62.5177 

.5 
.6 
.7 
.8 
.9 

471.4352 
475.2916 
479.1636 
483.0513 
486.9547 

76.9690 
77.2832 
77.5973 
77.9115 
78.2257 

.5 

.6 
.7 
.8 
.9 

683.4928 
688.1345 
692.7919 
697.4650 
702.1538 

92.6770 
92.9911 
93.3053 
93.6195 
93.9336 

177 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  J^  to  99,  advancing  by  Tenths 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum.  [ 

109.9557 
110.2699 
110.5841 
110.8982 
111.2124 

Diam. 

40.0 
.1 
.2 
.3 
.4 

Area. 

Circum. 

30.0 
.1 
.2 
.3 
.4 

706.8583 
711.5786 
716.3145 
721.0662 
725.8336 

94.2478 
94.5619 
94.8761 
95.1903 
95.5044 

35.0 
.1 
.2 
.3 
.4 

962.1128 
967.6184 
973.1397 
978.6768 
984.2296 

1256.6371 
1262.9281 
1269.2348 
1275.5573 
1281.8955 

125.6637 
125.9779 
126.2920 
126.6062 
126.9203 

.5 
.6 
.7 
.8 
.9 

730.6167 
735.4154 
740.2299 
745.0601 
749.9060 

95.8186 
96.1327 
96.4469 
96.7611 
97.0752 

.5 
.6 

.7 
.8 
.9 

989.7980 
995.3822 
1000.9821 
1006.5977 
1012.2290 

] 11.5265 
111.8407 
112.1549 
112.4690 
112.7832 

.5 
.6 

.7 
.8 
.9 

1288.2493 
1294.6189 
1301.0042 
1307.4052, 
1313.8219 

127.2345 
127.5487 
127.8628 
128.1770 
128.4911 

31.0 
.1 
.2 
.3 
.4 

754.7676 
759.6450 
764.5380 
769.4467 
774.3712 

97.3894 
97.7035 
98.0177 
98.3319 
98.6460 

36.0 
.1 
.2 
.3 
.4 

1017.8760 
1023.5387 
1029.2172 
1034.9113 
1040.6212 

113.0973 
113.4115 
113.7257 
114.0398 
114.3540 

41.0 
.1 
.2 
.3 
.4 

1320.2543 
1326.7024 
1333.1663 
1339.6458! 
1346.1410 

128.8053 
129.1195 
129.4336 
129.7478 
130.0619 

.5 
.6 
.7 
.8 
.9 

779.3113 
784.2672 
789.2388 
794.2260 
799.2290 

98.9602 
99.2743 
99.5885 
99.9026 
100.2168 

.5 
.6 

.7 
.8 
.9 

1046.3467 
1052.0880 
1057.8449 
1063.6176 
1069.4060 

114.6681 
114.9823 
115.2965 
115.6106 
115.9248 

.5 
.6 
.7 
.8 
.9 

1352.6520 
1359.1786 
1365.7210 
1372.2791 
1378.8529 

130.3761 
130.6903 
131.0044 
131.3186 
131.6327 

32.0 
.1 
.2 
.3 
.4 

804.2477 
809.2821 
814.3322 
819.3980 
824.4796 

100.5310 
100.8451 
101.1593 
101.4734 
101.7876 

37.0 
.1 
.2 
.3 
.4 

1075.2101 
1081.0299 
1086.8654 
1092.7166 
1098.5835 

116.2389 
116.5531 
116.8672 
117.1814 
117.4956 

42.0 
.1 
.2 
.3 
.4 

1385.4424 
1392.0476 
1398.6685 
1405.3051 
1411.9574 

131.9469 
132.2611 
132.5752 
132.8894 
133.2035 

.5 
.6 
.7 
.8 
.9 

829.5768 
834.6898 
839.8185 
844.%28 
850.1229 

102.1018 
102.4159 
102.7301 
103.0442 
103.3584 

.5 
.6 
.7 
.8 
.9 

1104.4662 
1110.3645 
1116.2786 
1122.2083 
1128.1538 

117.8097 
118.1239 
118.4380 
118.7522 
119.0664 

.5 
.6 
.7 
.8 
.9 

1418.6254 
1425.3092 
1432.0086 
1438.7238 
1445.4546 

133.5177 
133.8318 
134.1460 
134.4602 
134.7743 

33.0 
.1 
.2 
.3 
.4 

855.2986 
860.4902 
865.6973 
870.9202 
876.1588 

103.6726 
103.9867 
104.3009 
104.6150 
104.9292 

38.0 
.1 
.2 
.3 
.4 

1134.1149 
1140.0918 
1146.0844 
1152.0927 
1158.1167 

119.3805 
119.6947 
120.0088 
120.3230 
120.6372 

43.0 
.1 
.2 
.3 
.4 

1452.2012 
1458.%35 
1465.7415 
1472.5352 
1479.3446 

135.0885 
135.4026 
135.7168 
136.0310 
136.3451 

.5 
.6 
.7 
.8 
.9 

881.4131 
886.6831 
891.9688 
897.2703 
902.5874 

105.2434 
105.5575 
105.8717 
106.1858 
106.5000 

.5 
.6 
.7 
.8 
.9 

1164.1564 
1170.2118 
1176.2830 
1182.3698 
1188.4724 

120.9513 
121.2655 
121.5796 
121.8938 
122.2080 

.5 
.6 
.7 
.8 
.9 

1486.1697 
1493.0105 
1499.8670 
1506.7393 
1513.6272 

136.6593 
136.9734 
137.2876 
137.6018 
137.9159 

34.0 
.1 
.2 
.3 
.4 

907.9203 
913.2688 
918.6331 
924.0131 
929.4088 

106.8142 
107.1283 
107.4425 
107.7566 
108.0708 

39.0 
.1 

i 

.4 

1194.5906 
1200.7246 
1206.8742 
1213.0396 
1219.2207 

122.5221 
122.8363 
123.1504 
123.4646 
123.7788 

44.0 
.1 
.2 
.3 
.4 

1520.5308 
1527.4502 
1534.3853 
1541.3360 
1548.3025 

138.2301 
138.5442 
138.8584 
139.1726 
139.4867 

.5 
.6 
.7 
.8 
.9 

934.8202 
940.2473 
945.6901 
951.1486 
956.6228 

108.3849 
108.6991 
109.0133 
109.3274 
109.6416 

.5 
.6 
.7 
.8 
.9 

1225.417= 
1231.630C 
1237.8582 
1244.1021 
1250.3617 

124.0929 
124.4071 
124.7212 
125.0354 
125.3495 

.5 
.6 
.7 
.8 
.9 

1555.2847 
1562.2826 
1569.2962 
1576.3255 
1583.3706 

139.8009 
140.1153 
140.4292 
140.7434 
141.0575 

178 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  ^'^  to  99,  advancing  by  Tentlis 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

45.0 
.1 
.2 
.3 
.4 

1590.4313 
1597.5077 
1604.5999 
1611.7077 
1618.8313 

141.3717 
141.6858 
142.0000 
142.3142 
142.6283 

50.0 
.1 
.2 
.3 
.4 

1963.4954 
1971.3572 
1979.2348 
1987.1280 
1995.0370 

157.0796 
157.3938 
157.7080 
158.0221 
158.3363 

55.0 
.1 
.2 
.3 
.4 

2375.8294 
2384.4767 
2393.1396 
2401.8183 
2410.5126 

172.7876 
173.1017 
173.4159 
173.7301 
174.0442 

.5 
.6 

.7 
.8 
.9 

1625.9705 
1633.1255 
1640.2962 
1647.4826 
1654.6847 

142.9425 
143.2566 
143.5708 
143.8849 
144.1991 

.5 
.6 
.7 
.8 
.9 

2002.9617 
2010.9020 
2018.8581 
2026.8299 
2034.8174 

158.6504 
158.9646 
159.2787 
159.5929 
159.9071 

.5 
.6 

.7 
.8 
.9 

2419.2227 
2427.9485 
2436.6899 
2445.4471 
2454.2200 

174.3584 
174.6726 
174.9867 
175.3009 
175.6150 

46.0 
.1 
.2 
.3 

.4 

1661.9025 
1669.1360 
1676.3853 
1683.6502 
1690.9308 

144.5133 
144.8274 
145.1416 
145.4557 
145.7699 

51.0 
.1 
.2 
.3 
.4 

2042.8206 
2050.8395 
2058.8742 
2066.9245 
2074.9905 

160.2212 
160.5354 
160.8495 
161.1637 
161.4779 

56.0 
.1 
.2 
.3 
.4 

2463.0086 
2471.8130 
2480.6330 
2489.4687 
2498.3201 

175.9292 
176.2433 
176.5575 
176.8717 
177.1858 

.5 
.6 
.7 
.8 
.9 

1698.2272 
1705.5392 
1712.8670 
1720.2105 
1727.5697 

146.0841 
146.3982 
146.7124 
147.0265 
147.3407 

.5 
.6 
.7 
.8 
.9 

2083.0723 
2091.1697 
2099.2829 
2107.4118 
2115.5563 

161.7920 
162.1062 
162.4203 
162.7345 
163.0487 

.5 
.6 
.7 
.8 
.9 

2507.1873 
2516.0701 
2524.9687 
2533.8830 
2*42.8129 

177.5000 
177.8141 
178.1283 
178.4425 
178.7566 

47.0 
.1 
.2 
.3 
.4 

1734.9445 
1742.3351 
1749.7414 
1757.1635 
1764.6012 

147.6550 
147.9690 
148.2832 
148.5973 
148.9115 

52.0 
.1 
.2 
.3 

.4 

2123.7166 
2131.8926 
2140.0843 
2148.2917 
2156.5149 

163.3628 
163.6770 
163.9911 
164.3053 
164.6195 

57.0 
.1 
.2 
.3 
.4 

2551.7586 
2560.7200 
2569.6971 
2578.6899 
2587.6985 

179.0708 
179.3849 
179.6991 
180.0133 
180.3274 

.5 
.6 
.7 
.8 
.9 

1772.0546 
1779.5237 
1787.0086 
1794.5091 
1802.0254 

149.2257 
149.539S 
149.8540 
150.1681 
150.4823 

.5 
.6 
.7 
.8 
.9 

2164.7537 
2173.0082 
2181.2785 
2189.5644 
2197.8661 

164.9336 
165.2479 
165.5619 
165.8761 
166.1903 

.5 
.6 
.7 
.8 
.9 

2596.7227 
2605.7626 
2614.8183 
2623.8896 
2632.9767 

180.6416 
180.9557 
181.2699 
181.5841 
181.8982 

48.0 
.1 
.2 
.3 

.4 

1809.5574 
1817.1050 
1824.6684 
1832.2475 
1839.8423 

150.7964 
151.1106 
151.4248 
151.7389 
152.0531 

53.0 
.1 
.2 
.3 
.4 

2206.1834 
2214.5165 
2222.8653 
2231.2298 
2239.6100 

166.5044 
166.8186 
167.1327 
167.4469 
167.7610 

58.0 
.1 
.2 
.3 
.4 

2642.0794 
2651.1979 
2660.3321 
2669.4820 
2678.6476 

182.2124 
182.5265 
182.8407 
183.1549 
183.4690 

.5 
.6 
.7 
.8 
.9 

1847.4528 
1855.0790 
1862.7210 
1870.3786 
1878.0519 

152.3672 
152.6814 
152.9956 
153.3097 
153.6239 

.5 
.6 

.7 
.8 
.9 

2248.0059 
2256.4175 
2264.8448 
2273.2879 
2281.7466 

168.0752 
168.3894 
168.7035 
169.0177 
169.3318 

.5 
.6 
.7 
.8 
.9 

2687.8289 
2697.0259 
2706.2386 
2715.4670 
2724.7112 

183.7832 
184.0973 
184.4115 
i84.7256 
185.0398 

49.0 
.1 
.2 
.3 
.4 

1885.7409 
1893.4457 
1901.1662 
190S.9024 
1916.6543 

153.9380 
154.2522 
154.5664 
154.8805 
155.1947 

54.0 
.1 

i 

.4 

2290.2210 
2298.7112 
2307.2171 
2315.7386 
2324.2759 

169.6460 
169.9602 
170.2743 
170.5885 
170.9026 

59.0 
.1 

.2 
.3 
.4 

2733.9710 
2743.2466 
2752.5378 
2761.8448 
2771.1675 

185.3540 
185.6681 
185.9823 
186.2964 
186.6106 

.5 

.6 
.7 
.8 
.9 

1924.4218 
1932.2051 
1940.0042 
1947.8189 
1955.6493 

155.5088 
155.8230 
156.1372 
156.4513 
156.7655 

.5 
.6 
-.7 
.8 
.9 

2332.8289 
2341.3976 
2349.9820 
2358.5821 
2367.1979 

171.2168 
171.5310 
171.8451 
172.1593 
172.4735 

.5 
.6 
.7 
.8 
.9 

2780.5058 
2789.8599 
2799.2297 
2808.6152 
2818.0165 

186.9248 
187.2389 
187.5531 
187.8672 
189.1814 

179 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  J^  to  99,  advancing  by  Tenths 


Diam.   Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

60.0 
.1 
.2 
.3 
.4 

2827.4334 
2836.8660 
2846.3144 
2855.7784 
2865.2582 

18S.4956 
188.8097 
189.1239 
189.4380 
189.7522 

65.0 
.1 
.2 
.3 
.4 

3318.3072 
3328.5253 
3338.7590 
3349.0085 
3359.2736 

204.2035 
204.5176 
204.8318 
205.1460 
205.4602 

70.0 
.1 
.2 
.3 
.4 

3848.4510 
3859.4544 
3870.4736 
3881.5084 
3892.5590 

219.9115 
220.2256 
220.5398 
220.8540 
221.1681 

.5 
.6 
.7 
.8 
.9 

2874.7536 
2884.2648 
2893.7917 
2903.3343 
2912.8926 

190.0664 
190.3805 
190.6947 
191.0088 
191.3230 

.5 
.6 
.7 
.8 
.9 

3369.5545 
3379.8510 
3390.1633 
3400.4913 
3410.8350 

205.7743 
206.0885 
206.4026 
206.7168 
207.0310 

.5 
.6 

.7 
.8 
.9 

3903.6252 
3914.7072 
3925.8049 
3936.9182 
3948.0473 

221.4823 
221.7964 
222.1106 
222.4248 
222.7389 

61.0 
.1 
.2 
.3 

.4 

2922.4666 
2932.0563 
2941.6617 

2951.2828 
2960.9197 

191.6372 
191.9513 
192.2655 
192.5796 
192.8938 

66.0 
.1 
.2 
.3 
.4 

3421.1944 
3431.5695 
3441.9603 
3452.3669 
3462.7891 

207.3451 
207.6593 
207.9734 
208.2876 
208.6017 

71.0 
.1 
.2 
.3 
.4 

3959.1921 
3970.3526 
3981.5289 
3992.7208 
4003.9284 

223.0531 
223.3672 
223.6814 
223.9956 
224.3097 

.5 
.6 
.7 
.8 
.9 

2970.5722 
2980.2405 
2989.9244 
2999.6241 
3009.3395 

193.2079 
193.5221 
193.8363 
194.1504 
194.4646 

.5 
.6 
.7 
.8 
.9 

3473.2270 
3483.6807 
^494.1500 
3504.6351 
3515.1359 

208.9159 
209.2301 
209.5442 
209.8584 
210.1725 

.5 
.6 

.7 
.8 
.9 

4015.1518 
4026.3908 
4037.6456 
4048.9160 
4060.2022 

224.6239 
224.9380 
225.2522 
225.5664 
225.8805 

62.0 
.1 
.2 
.3 
.4 

3019.0705 
3028.8173 
3038.5798 
3048.3580 
305S.1520 

194.7787 
195.0929 
195.4071 
195.7212 
196.0354 

67.0 
.1 
.2 
.3 

.4 

3525.6524 
3536.1845 
3546.7324 
3557.2960 
3567.8754 

210.4867 
210.8009 
211.1150 
211.4292 
211.7433 

72.0 
.1 
.2 
.3 
.4 

4071.5041 
4082.8217 
4094.1550 
4105.5040 
4116.8687 

226.1947 

226.5088 
226.8230 
227.1371 
227.4513 

.5 
.6 
.7 
.8 
.9 

3067.9616 
3077.7869 
3087.6279 
3097.4847 
3107.3571 

196.3495 
196.6637 
196.9779 
197.2920 
197.6062 

.5 
.6 
.7 
.8 
.9 

3578.4704 
3589.0811 
3599.7075 
3610.3497 
3621.0075 

212.0575 
212.3717 
212.6858 
213.0000 
213.3141 

.5 
.6 
.7 
.8 
.9 

4128.2491 
4139.6452 
4151.0571 
4162.4846 
4173.9279 

227.7655 
228.0796 
228.3938 
228.7079 
229.0221 

63.0 
.1 
.2 
.3 
.4 

3117.2453 
3127.1492 
3137. 068S 
3147.0040 
3156.9550 

197.9203 
198.2345 
19S.54S7 
198.8628 
199.1770 

68.0 
.1 
.2 
.3 
.4 

3631.6811 
3642.3704 
3653.0754 
3663.7960 
3674.5324 

213.6283 
213.9425 
214.2566 
214.5708 
214.8849 

73.0 
.1 
.2 
.3 
.4 

4185.3868 
4196.8615 
4208.3519 
4219.8579 
4231.3797 

229.3363 
229.6504 
229.9646 
230.2787 
230.5929 

.5 

.6 
.7 
.8 
.9 

3166.9217 
3176.9043 
3186.9023 
3196.9161 
3206.9456 

199.4911 
199.8053 
200.1195 
200.4336 
200.7478 

.5 
.6 

.7 
.8 
.9 

3685.2845 
3696.0523 
3706.8359 
3717.6351 
3728.4500 

215.1991 
215.5133 
215.8274 
216.1416 
216.4556 

.5 
.6 
.7 
.8 
.9 

4242.9172 
4254.4704 
4266.0394 
4277.6240 
4289.2243 

230.9071 
231.2212 
231.5354 
231.8495 
232.1637 

64.0 
.1 
.2 
.3 
.4 

3216.9909 
3227.0518 
3237. 12S5 
3247.2222 
3257.3289 

201.0620 
201.3761 
201.6902 
202.0044 
202.3186 

69.0 
.1 
.2 
.3 
.4 

3739.2807 
3750.1270 
3760.9891 
3771.8668 
3782.7603 

216.7699 
217.0841 
217.3982 
217.7124 
218.0265 

74.0 
.1 
.2 
.3 
.4 

4300.8403 
4312.4721 
4324.1195 
4335.7827 
4347.4616 

232.4779 
232.7920 
233.1062 
233.4203 
233.7345 

.5 
.6 
.7 

.8 
.9 

3267.4527 
3277.5922 
3287.7474 
3297.9183 
3308.1049 

202.6327 
202.9469 
203.2610 
203.5752 
203.8894 

.5 
.6 

.7 
.8 
.9 

3793.6695 
3804.5944 
3815.5350 
3826.4913 
3837.4633 

218.3407 
218.6548 
218.9690 
219.2832 
219.5973 

.5 
.6 
.7 
.8 
.9 

4359.1562 

4370.8664 
4382.5924 
4394.3341 
4406.0916 

234.0487 
234.3628 
234.6770 
234.9911 
235.3053 

180 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  J^  to  99,  advancing  by  Tenths 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

75.0 
.1 
.2 
.3 
.4 

4417.8647 
4429.6535 
4441.4580- 
4453.2783 
4465.1142 

235.6194 
235.9336 
236.2478 
236.5619 
236.8761 

80.0 
.1 
.2 
.3 
.4 

5026.5482 
5039.1225 
5051.7124 
5064.3180 
5076.9394 

251.3274 
251.6416 
251.9557 
252.2699 
252.5840 

85.0 
.1 
.2 
.3 
.4 

5674.5017 
5687.8614 
5701.2367 
5714.6277 
5728.0345 

267.0354 
267.3495 
267.6637 
267.9779 
268.2920 

.5 
.6 

.7 
.8 
.9 

4476.9659 
4488.8332 
4500.7163 
4512.6151 
4524.5296 

237.1902 
237.5044 
237.8186 
238.1327 
238.4469 

.5 
.6 
.7 
.8 
.9 

5089.5764 
5102.2292 
5114.8977 
5127.5819 
5140.2818 

252.8982 
253.2124 
253.5265 
253.8407 
254.1548 

.5 

:f 

.8 
.9 

5741.4569 
5754.8951 
5768.3490 
5781.8185 
5795.3038 

268.6062 
268.9203 
269.2345 
269.5486 
269.8628 

76.0 
.1 
.2 
.3 
.4 

4536.4598 
4548.4057 
4560.3673 
4572.3446 
4584.3377 

238.7610 
239.0752 
239.3894 
239.7035 
240.0177 

81.0 
.1 
.2 
.3 
.4 

5152.9973 
5165.7287 
5178.4757 
5191.2384 
5204.0168 

254.4690 
254.7832 
255.0973 
255.4115 
255.7256 

86.0 
.1 
.2 
.3 
.4 

5808.8048 
5822.3215 
5S35.8539 
5849.4020 
5862.9659 

270.1770 
270.4911 
270.8053 
271.1194 
271.4336 

.5 
.6 
.7 
.8 
.9 

4596.3464 
4608.3708 
4620.4110 
4632.4669 
4644.5384 

240.3318 
240.6460 
240.9602 
241.2743 
241.5885 

.5 
.6 
.7 
.8 
.9 

5216.8110 
5229.6208 
5242.4463 
5255.2876 
5268.1446 

256.0398 
256.3540 
256.6681 
256.9823 
257.2966 

.5 
.6 
.7 
.8 
.9 

5876.5454 
5890.1407 
5903.7516 
5917.3783 
5931.0206 

271.7478 
272.0619 
272.3761 
272.6902 
273.0044 

77.0 
.1 
.2 
.3 
.4 

4656.6257 
4668.7287 
4680.8474 
4692.9818 
4705.1319 

241.9026 
242.2168 
242.5310 
242.8451 
243.1592 

82.0 
.1 
.2 
.3 
.4 

5281.0173 
5293.9056 
5306.8097 
5319.7295 
5332.6650 

257.6106 
257.9247 
258.2389 
258.5531 
258.8672 

87.0 
.1 
.2 
.3 
.4 

5944.6787 
5958.3525 
5972.0420 
5985.7472 
5999.4681 

273.3186 
273.6327 
273.9469 
274.2610 
274.5752 

.5 
.6 

.7 
.8 
.9 

4717.2977 
4729.4792 
4741.6765 
4753.8894 
4766.1181 

243.4734 
243.7876 
244.1017 
244.4159 
244.7301 

.5 

.6 
.7 
.8 
.9 

5345.6162 
5358.5832 
5371.5658 
5384.5641 
5397.5782 

259.1814 
259.4956 
259.8097 
260.1239 
260.4380 

.5 
.6 
.7 
.8 
.9 

6013.2047 
6026.9570 
6040.7250 
6054.5088 
6068.3082 

274.8894 
275.2035 
275.5177 
275.8318 
276.1460 

78.0 
.1 
.2 
.3 
.4 

4778.3624 
4790.6225 
4802.8983 
4815.1897 
4827.4969 

245.0442 
245.3584 
245.6725 
245.9867 
246.3009 

83.0 
.1 
.2 
.3 
.4 

5410.6079 
5423.6534 
5436.7146 
5449.7915 
5462.8840 

260.7522 
261.0663 
261.3805 
261.6947 
262.0088 

88.0 
.1 
.2 
.3 
.4 

6082.1234 
6095.9542 
6109.8008 
6123.6631 
6137.5411 

276.4602 
276.7743 
277.0885 
277.4026 
277.7168 

.5 
.6 
.7 
.8 
.9 

4839.8198 
4852.1584 
4864.5128 
4876.8828 
4889.2685 

246.6150 
246.9292 
247.2433 
247.5575 
247.8717 

.5 
.6 

.7 
.8 
.9 

5475.9923 
5489.1163 
5502.2561 
5515.4115 
5528.5826 

262.3230 
262.6371 
262.9513 
263.2655 
263.5796 

.5 
.6 
.7 
.8 
.9 

6151.4348 
6165.3442 
6179.2693 
6193.2101 
6207.1666 

278.0309 
278.3451 
278.6593 
278.9740 
279.2876 

79.0 
.1 
.2 
.3 
.4 

4901.6699 
4914.0871 
4926.5199 
4938.9685 
4951.4328 

248.1858 
248.5000 
248.8141 
249.1283 
249.4425 

84.0 
.1 
.2 
.3 
.4 

5541.7694 
5554.9720 
5568.1902 
5581.4242 
5594.6739 

263.8938 
264.2079 
264.5221 
264.8363 
265.1514 

89.0 
.1 
.2 
.3 
.4 

6221.1389 
6235.1268 
6249.1304 
6263.1498 
6277.1849 

279.6017 
279.9159 
280.2301 
280.5442 
2S0.85S4 

.5 
.6 
.7 
.8 
.9 

4963.9127 
4976.4084 
4988.9198 
5001.4469 
5013.9897 

249.7566 
250.0708 
250.3850 
250.6991 
251.0133 

.5 
.6 
.7 
.8 
.9 

5607.9392 
5621.2203 
5634.5171 
5647.8296 
5661.1578 

265.4646 
265.7787 
266.0929 
266.4071 
266.7212 

.5 
.6 
.7 
.8 
.9 

6291.2356 
6305.3021 
6319.3843 
6333.4822 
6347.5958 

281.1725 
281.4867 
281.8009 
282.1150 
282.4292 

TABLES 


181 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES 

For  Diameters  from  J^  to  99,  advancing  by  Tenths 


Diam. 

Area.      ,   Circum. 

Diam. 

Area. 

Circum. 

Diam. 

%.o 

.1 
.2 
.3 
.4 

Area. 

Circum. 

90.0 
.1 
.2 
.3 
.4 

6361.7251!  282.7433 
6375.8701  j  283.0575 
6390.0309  283.3717 
6404.2073  283.6858 
6418.3995   284.0000 

93.0 
.1 
.2 
.3 
.4 

6792.9087 
6807.5250 
6822.1569 
6836.8046 
6851.4680 

292.1681 
292.4823 
292.7964 
293.1106 
293.4248 

7238.2295 

7253.3170 
7268.4202 
7283.5391 
7298.6737 

301.5929 
301.9071 
302.2212 
302.5354 
302.8405 

.5 
.6 
.7 
.8 
.9 

6432.6073   284.3141 
6446.8309,  284.6283 
6461.0701    284.9425 
6475.3251   285.2566 
6489.5958j  285.5708 

.5 

.6 
.7 
.8 
.9 

6866.1471 
6880.8419 
6895.5524 
6910.2786 
6925.0205 

293.7389 
294.0531 
294.3672 
294.6814 
294.9956 

.5 
.6 
.7 
.8 
.9 

7313.8240 
7328.9901 
7344.1718 
7359.3693 
7374.5824 

303.1637 
303.4779 
303.7920 
304.1062 
304.4203 

91.0 
.1 
.2 
.3 
.4 

6503.8S22  285.8849 
6518.1843   286.1991 
6532.5021    286.5133 
6546.8356  286.8274 
6561.1848  287.1416 

94.0 
.1 
.2 
.3 
.4 

6939.7782 
6954.5515 
6969.3106 
6984.1453 
6998.9658 

295.3097 
295.6239 
295.9380 
296.2522 
296.5663 

97.0 
.1 
.2 
.3 
.4 

7389.8113 
7405.0559 
7420.3162 
7435.5922 
7450.8839 

304.7345 
305.04S6 
305.3628 
305.6770 
305.9911 

.5 
.6 

.7 
.8 
.9 

6575.5498 
6589.9304 
6604.3268 
6618.7388 
6633.1666 

287.4557 
287.7699 
288.0840 
288.3982 
288.7124 

.5 
.6 
.7 
.8 
.9 

7013.8019 
7028.6538 
7043.5214 
7058.4047 
7073.3033 

296.8805 
297.1947 
297.5088 
297.8230 
298.1371 

.5 
.6 
.7 
.8 
.9 

7466.1913 
7481.5144 
7496.8532 
7512.2078 
7527.5780 

306.3053 
306.6194 
306.9336 
307.2478 
307.5619 

92.0 
.1 
.2 
.3 
.4 

6647.6101 
6662.0692 
6676.5441 
6691.0347 
6705.5410 

289.0265 
289.3407 
289.6548 
289.9690 
290.2832 

95.0 

i 

.3 
.4 

7088.2184 
7103.1488 
7118.1950 
7133.0568 
7148.0343 

298.4513 
298.7655 
299.0796 
299.3938 
299.7079 

98.0 
.1 
.2 
.3 
.4 

7542.9640 
7558.3656 
7573.7830 
7589.2161 
7604.6648 

307.8761 
308.1902 
308.5044 
308.8186 
309.1327 

.5 
.6 
.7 
.8 
.9 

6720.0630 
6734.6C08 
6749.1542 
6763.7233 
6778.30S2 

290.5973 
290.9115 
291.2256 
291.5398 
291.8540 

.5 
.6 

.7 
.8 
.9 

7163.0276 
7178.0366 
7193.0612 
7208.1016 
7223.1577 

300.0221 
300.3363 
300.6504 
300.9646 

301.2787 

.5 
.6 
.7 
.8 
.9 

7620.1293 
7635.6095 
7651.1054 
7666.6170 
7682.1444 

309.4469 
309.7610 
310.0752 
310.3894 
310.7035 

DECIMAL  EQUIVALENTS  OF  FRACTIONS  OF  ONE  INCH 


1-64 

.015625   j 

17-64 

.265625     ' 

33-64 

.515625 

49-64 

.765625 

1-32 

.03125     ! 

9-32 

.28125 

17-32 

.53125 

25-32 

.78125 

3-64 

.046875 

19-64 

.296875 

35-64 

.546875 

51-64 

.796875 

1-16 

.0625 

5-16 

.3125 

9-16 

.5625       ; 

13-16 

.8125 

5-64 

.078125 

21-64 

.328125 

37-64 

.578125 

53-64 

.828125 

3-32 

.09375 

11-32 

.34375 

19-32 

.59375     i 

27-32 

.84375 

7-64 

.109375 

23-64 

.359375 

39-64 

.609375    1 

55-64 

.859375 

1-8 

.125 

3-8 

.375 

5-8 

.625         1 

7-8 

.875 

9-64 

.140625 

25-64 

.390625 

41-64 

.&t0625 

57-64 

.890625 

5-32 

.15625 

13-32 

.40625 

21-32 

.65625 

29-32 

.90625 

11-64 

.171875 

27-64 

.421875 

43-64 

.671875 

59-64 

.921875 

3-16 

.1875 

■7-16 

.4375 

11-16 

.6875 

15-16 

.9375 

13-64 

.203125 

29-64 

.453125 

45-64 

.703125 

61-64 

.953125 

7-32 

.21875 

15-32 

.46875 

23-32 

.71875 

31-32 

.96875 

15-64 

.234375 

31-^4 

.484375 

47-64 

.734375 

63-64 

.984375 

1-4 

.25 

1-2 

.50 

3-4 

.75 

1 

1. 

182 


TABLES 


WEIGHT  OF  A  CUBIC  FOOT  OF  WATER  BETWEEN 
32°  AND  212°  F 


Temper- 

Weight, 

Temper- 

Weight, 

Temper- 

Weight, 

ature 

lbs.  per 

ature 

lbs.  per 

ature 

lbs.  per 

Fahr. 

cubic  foot 

Fahr. 

cubic  foot 

Fahr. 

cubic  foot 

32° 

62.42 

123° 

61.68 

168° 

60.81 

35 

62.42 

124 

61.67 

169 

60  79 

40 

62.42 

125 

61.65 

170 

60.77 

45 

62.42 

126 

61.63 

171 

60.75 

50 

62.41 

127 

61.61 

172 

60.73 

52 

62.40 

128 

61.60 

173 

60.70 

54 

62.40 

129 

61.58 

174 

60.68 

56 

62.39 

130 

6r.56 

175 

60.66 

58 

62.38 

131 

61.54 

176 

60.64 

60 

62.37 

132 

61.52 

177 

60.62 

62 

62.36 

133 

61.51 

178 

60.59 

64 

62.35 

134 

61.49 

179 

60.57 

66 

62.34 

135 

61.47 

180 

60.55 

68 

62.33 

136 

61.45 

181 

60.53 

70 

62.31 

137 

61.43 

182 

60.50 

72 

62.30 

138 

61.41 

183 

60  48 

74 

62.28 

139 

61.39 

184 

60.46 

76 

62.27 

140 

61.37 

185 

60.44 

78 

62.25 

141 

61.36 

186 

60.41 

80 

62.23 

142 

61.34 

187 

60  39 

82 

62.21 

143 

61.32 

188 

60.37 

84 

62.19 

144 

61.30 

189 

60.34 

86 

62.17 

,145 

61.28 

190 

60.32 

88 

62.15 

146 

61  26 

191 

60.29 

90 

62.13 

147 

61.24 

192 

60.27 

92 

62.11 

148 

61.22 

193 

60.25 

94 

62.09 

149 

61.20 

194 

60.22 

96 

62  07 

150 

61.18 

195 

60.20 

98 

62.05 

151 

61.16 

196 

60.17 

100 

62.02 

152 

61.14 

197 

60.15 

102 

62.00 

153 

61.12 

198 

60.12 

104 

61.97 

154 

61.10 

199 

60.10 

106 

61.95 

155 

6108 

200 

60.07 

108 

61.92 

156 

61.06 

201 

60.05 

110 

61.89 

157 

61.04 

202 

60.02 

112 

61.86 

158 

61.02 

203 

60.00 

113 

61.84 

159 

61.00 

204 

59.97 

114 

61.83 

160 

60.98 

205 

59.95 

115 

61.82 

161 

60.96 

206 

59.92 

116 

61.80 

162 

60.94 

207 

59.89 

117 

61.78 

163 

60.92 

208 

59.87 

118 

61.77 

164 

60.90 

209 

59.84 

119 

61.75 

165 

60.87 

210 

59.82 

120 

61.74 

166 

60.85 

211 

59.79 

121 

61.72 

167 

60.83 

212 

59.76 

122 

61.70 

WEIGHT  OF  A  CUBIC  FOOT  OF  WATER  AT  HIGH 
TEMPERATURES 


Tem- 
pera- 
ture 
Fahr. 

Weight  of 

1  cubic 

foot 

Differ- 
ence 
per  1 

degree 

Tem- 
pera- 
ture 
Fahr. 

Weight  of 
1  cubic 
foot 

Differ- 
ence 
per  1 

degree 

Tem- 
pera- 
ture 
Fahr. 

Weight  of 
1  cubic 
foot 

Differ- 
ence 
per  1 

degree 

220'^ 

230 

240 

250 

260 

270 

280 

59.641 
59.372 
59.096 
58.812 
58.517 
58.214 
57.903 

0.0253 
0.0269 
0.0276 
0  0284 
0.0295 
0.0303 
0.0311 

290° 

300 

310 

320 

330 

340 

57.585 
57.259 
56.925 
56.584 
56.236 
55.883 

0.0318 
0.0326 
0.0334 
0.0341 
0.0348 
0.0353 

350" 

360 

370 

380 

390 

400 

55.523 
55.158 
54.787 
54.411 
54.030 
53.635 

0.0360 
0.0365 
0.0371 
0.0376 
0,0381 
0.0395 

■980 


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APPENDIX 


APPENDIX 

COUNTERS,   GAGES,  AND  OTHER  ACCESSORY 
APPARATUS 


THE  CROSBY   REVOLUTION   COUNTER  OR 
ENGINE  REGISTER 

Patented 


Engine  Revolution  Counters,  as 
commonly  designed  and  constructed, 
depend  iipon  an  escapement  for  re- 
cei\ang  the  actuating  force,  and  a 
star-toothed  wheel  for  transmitting 
the  movement  to  the  figure-.wheels. 
The  escapement  principle,  while  well 
adapted  to  a  delicate  machine  actuated  by  a  constant  force, 
like  a  watch  or  clock,  is  ill  suited  to  a  counter  for  registering 
the  stroke  of  a  steam  engine  or  other  ponderous  macliine, 
where  the  actuating  force  may  be  out  of  all  suitable  propor- 
tion to  the  structural  strength  of  the  counter,  and  such  as 
to  destroy  it,  if  from  any  cause,  like  the  varying  sti'oke  of  a 
piunp,  the  pallet  fails  to  properly  engage  with  the  tooth  of 
the  wheel.  From  the  same  causes  such  counters  may  also 
fail  to  register.  These  facts  are  well  known  to  all  mechanics 
who  have  had  experience  with  escapement  counters.  To 
forcibly  illustrate  how  poorly  adapted  to  a  counter  the 
escapement  principle  is,  it  is  only  necessary  to  state,  that  in 
a  watch,  by  the  slight  force  of  the  actuating  s])ring  or 
weight,    it    simply  perviitii   a   tooth   to   escape,  wliile    in    a 

185 


186  REVOLUTION  COUXTERS 

counter  it  is  required  to  move  the  irhole  nieehanifim.,  and  to 
do  this  intermittently  and  with  the  varying  resistance  of  one 
or  all  of  the  figure-wheels. 

In  a  Revolution  Counter  which  shall  he  rellaJile,  durahLe, 
and  free  from  liahility  to  serious  injury,  the  actuating  force 
must,  through  proper  mechanism,  he  transmitted  directly 
and  with  certamty  to  the  figure- wheels,  and  this  can  best  be 
done  by  means  of  a  crank.  It  matters  not  in  the  Crosby 
Counter  whether  the  movement  of  the  crank  is  rotary  or 
merely  oscillatory,  it  will  count  just  the  same. 

The  Crosby  Improved  Revolution  Counter,  only,  employs 
the  crank  principle,  applied  through  other  simple  mechanical 
motions,  so  as  to  record  with  certainty  the  operations  of  any 
machine,  and  at  the  same  time  obviate  all  danger  of  injury 
to  the  counter  itself  or  the  machine  to  which  it  is  attached. 

This  co^mter  is  adapted  to  either  right  or  left  hand  rotary 
or  reelprocatinfj  motions,  and  is  ca^pable  of  500  revolutions 
per  minute  with  safety  to  the  machine  and  accuracy  in  the 
enumeration. 

The  shaft  through  which  the  actuating  force  is  applied 
may  extend  from  the  counter  either  on  the  right-hand  or 
left-hand  side  as  desired. 

It  is  made  in  the  following  sizes  : 

12  inch  dial 8  wheels 

12  "  '' 7  " 

12  '•  " .  6  " 

10  "  " 8  " 

10  ••  "  .......  7  " 

10  '•  " ,     .•  6  " 

8i  '•  "  ■ 8  " 

81  "  " 7  " 

81  '•  - 6  " 

6i  -  "  .......  6  " 

6  "  " 6  " 


REVOLUTIOX  COUNTERS 


CROSBY  SQUARE  COUNTER 


187 


The  actuating  mechanism  of  this  counter  is  positive  and 
employs  the  principles  just  des(;rihe(:l,  as  used  in  the  Croshy 
Revolution  Counter.  It  is  a  strong  and  useful  instrument, 
compact  in  form,  durahle  and  accurate.  It  may  he  provided 
with  a  re-setting  device  and  also  with  a  padlock  if  desired. 
When    recpiired    for    rotary    motion,    it    should    he     stated 


U^ 


whether  it  is  to  he  used  for  right-hand  or  left-hand  rotation. 
This  counter  is  made  in  the  following  sizes  : 

4f  X  1^  in.  dial 4  figures 

5i  X  1^    ••     •• 5      " 

6X1^'-" 6      " 

7i  X  2^    ••     '^ 4      " 

8i  X  2]r    '•      •• 5       " 

9i  X  21    -     " 6      " 

lOf  X   2:^     "       " 7         " 


THE  CROSBY  LOCOMOTIVE  COUNTER 
For  High  Rotative  Speeds 

The  cut  on  ])age  18S  shows  the  Locomotive  CoHuter.  It 
is  designed  ])articularly  for  use  on  locomotives  and  higli  s])eed 
engines,  and  is  a  valuahle  auxiliary  to  the  steam  engine  in- 
dicator. The  arm  which  moves  the  ratchet  is  connected  hy 
a  cord  with  some  recipiocating  2)art  of  the   engine,  or  with 


188 


CROSBY  LOCOMOTIVE  COUI^^TER 


the  drum  motion,  so  as  to  give  it  about  1^  inches  swing 
back  and  forth  during  each  revohition  of  the  shaft.      It  is 


provided  with  a  convenient  starting  and  stopping  device,  so 
that  it  can  be  made  to  l)egin  or  stop  counting  at  any  instant. 

CROSBY  RECORDING  COUNTER 

Patented 

This  instrument  furnishes  a  chart  record  of  the  revolu- 
tions or  strokes  of  any  engine,  pump,  or  moving  part.  It  is 
designed    with    remarkable    genius  for  its  special  purpose, 


CROSBY  RECORDING  COUXTER 


189 


and  it  w-ill  record  the  highest  speeds  with  mathematical 
accuracy.  Every  counter  is  tested  to  at  least  two  thousand 
revolutions  per  minute,  and  will  give  positive  results  at  much 
higher  speeds  without  slip  or  error.  Each  regvilar  chart 
affords  a  pen  record  up  to  tifty  thousand  consecutive  strokes 
or  revolutions,  and  the  exact  total  nund)er,  or  the  elapsed 
count  between  any  two  noted  periods,  can  be  read  with  cer- 
tainty. The  highest  working  speeds  found  in  mechanical 
operations  are  within  the  range  of  this  device. 

The  Crosby  Recording  Counter  is  not  a  tachometer,  but  a 
chart-recording  instrument,  occupying  a  field  by  itself  of 
peculiar  importance.  There  is  no  other  instrument  like  it, 
or  that  gives  similar  results.  Its  applications  are  varied  and 
universal.  It  will  be  found  especially  valuable  in  making 
permanent  records  of  the  performance  of  mat^hinery  or 
engines  either  under  special  test  or  in  daily  service,  and  it  is 


of  the  greatest  usefidness  and  importance  to  every  engineer, 
designer,  and  user  of  power.  The  chart  is  8  inches  in  dia- 
meter and  easily  read ;  the  mechanism  is  well  constructed, 
durable,  and  accurate  ;  it  cannot  get  out  of  order  or  adjust- 
ment.    All  like  parts  are  interchangeable  and  suitably  de- 


190  PRKSSURE  GAGES 

signed  to  give  proper  wear  and  service.  It  is  adapted  for 
hoth  revolutions  and  reciprocating  motion  without  alteration. 
It  is  simple  to  attach  and  no  skill  is  required  to  operate  it. 

A  smaller  recording  counter  capable  of  registering  at  the 
highest  speeds  upon  a  chart  reading  to  5,000  revolutions  or 
strokes,  and  adapted  to  he  attached  to  the  Crosby  Reducing 
Wheel,  is  described  on  l)age  73. 

CROSBY   PRESSURE  AND  VACUUM    GAGES 
Im.poi'tant 

Accuracy  is  the  essential  feature  in  all  gages,  whether 
pressure  or  vacuum.  The  principle  of  construction  of 
Crosby  gages  is  correct  and  they  embody  important  improve- 
ments in  many  essential  details. 

In  the  Crosby  Improved  Pressure  Gage  the  tube  springs 
are  connected  at  each  end  with  their  respective  parts  by  screw 


threads,  without  tl>e  use  of  any  soldering  material  wliatever, 
thus  insuring  tight  joints  under  all  conditions  of  heat  and 
pressure. 

The  index  mechanism  and  the  dial  are  mounted  upon  an 
extension  of  the  socket,  thus  rendering  the  entire  operating 


EECORDIXa  OAGKS 


191 


parts  of  the  gage  independent  of  the  case  and  free  from  any 
errors  arising  from  its  distortion  or  from  external  heat. 

The  method  by  which  Crosby  gages  are  tested  and  grad- 
uated will  insure  a  truthful  and  reliable  gage.  Each  one  is 
tested  under  steam  pressure  and  subjected  to  pressures  accu- 
rately measui-ed  by  standardized  weights,  and  the  gage  is 
graduated  to  such  absolute  pressm'es  and  not  by  comparison 
only  with  another  gage. 

An  equally  accurate  method  is  used  in  the  testing  of 
vacuum  gages  ;  each  one  is  tried,  marked,  and  adjusted  by 
the  direct  readings  of  a  mercury  column,  by  means  of  an 
apparatus  in  wliich  the  successive  stages  of  vacumu  ai-e 
actually  produced. 

Every  gage  used  to  indicate  the  pressure^  of  steam  should 
have  a  siphon  or  some  other  device  which  wdll  furnish  water 
to  and  completely  fill  the  tube  springs  to  keep  them  cool. 
Be  sure  that  the  connections  between  the  gage  and  the 
siphon  are  perfectly  tight. 

CROSBY  PRESSURE  RECORDER 

Patented 


The   Crosby   Pressure  Recorder  records  the  pressure  of 
any  fluid  during  a  cex'tain  jieriod  of  time. 


192 


RECORDIXG  GAGES 


It  is  designed  to  supply  the  great  and  constantly  increas- 
ing demand  for  a  compact  and  reliable,  yet  not  too  costly, 
instrmiient  for  recording  all  the  variations  of  pressure  which 
take  place  in  a  steam  boiler  or  other  receptacle.  It  gives  a 
graphic  chart  showing  every  such  variation  of  pressure,  its 
extent  and  duration,  and  the  time  wheii  it  occurs.  The  case 
is  circular  and  is  uniform  in  appearance  with  the  other  in- 
struments usually  set  up  in  an  engine  room. 

The  socket  by  which  it  is  attached  to  the  boiler  extends 
upward  within  the  case,  and  supports  the  clock  and  other 
operating  parts,  thus    producing    a    unity    of  action  which 


gives  a  record  true  to  the  axis  of  the  chart  under  all  condi- 
tions. On  the  same  post  with  the  pen  lever  and  below  it, 
is  a  corresponding  lever  carrying  a  small  table  on  which 
rests  the  pen  point.  Between  the  pen  and  table  is  placed 
the  chart,  and  as  both  bear  upon  it  there  is  insured  a  con- 
tinuous contact  and  in  operation  a  continuous  line. 

The  pen  is  charged  with  a  supply  of  red  ink,  and  is  easily 
and  delicately  adjusted  to  the  surface  of  the  chart  by  an 
ingenious  device  at  its  base,  giving  records  of  unequaled 
legibility  and  accuracy. 


RECOKDIXG  GAGES  193 

CROSBY  PRESSURE  RECORDER  AND  GAGE 

Patented 


The  Crosby  Pressure  Recorder  and  Gage,  in  addition  to 
recording  the  pressure  of  any  fluid  during  a  certain  period 
of  tinie,  has  an  index  hand  and  an  outside  circle  of  figures 
to  show  the  actual  pressure  recorded  on  the  chart  at  the 
moment  of  observation ;  in  this  respect  it  ojjerates  like  an 
ordinary  steam  gage. 

The  chart  rotates  once  in  24  hours,  and  by  the  employ- 
ment of  a  special  clock  movement,  the  rotation  of  the  chart 
may  be  made  to  conform  to  any  period  of  time  from  one 
hour  to  one  week,  thus  adapting  the  instrimient  to  ahnost 
any  conditions  to  be  found,  in  which  a  record  of  pressures  is 
desirable  or  necessary  ;  and  the  range  of  pressures  which  may 
be  recorded  is  practically  unlimited. 

The  reading  of  the  chart,  as  shown  above,  is  110 
pounds  })ressure  at  6.30  o'clock  a.m.  Supposing  the  instru- 
ment to  be  properly  connected  to  a  steam  boiler,  or  other 
receptacle,  then  during  the  next  24  hours,  a  red  line  is 
traced  by  the  pen  completely  around  the  dial,  showing 
by  its  deviations  from  a  true  circle,  the  variations  of 
pressure  which  take  place  during  the  whole  of  that  time. 


194 


RECORDING  GAGES 


Special  Crosby  Recording  Gages  are  made  to  give  con- 
tinuous chart  records  of  the  working  pressures  in  air-brake 
reservoirs  and  train  lines,  and  in  the  cylinders  and  tanks  of 
puinps  and  hydraulic  presses. 

The  Crosby  Gas,  Mine,  and  Draft  Recorder  is  an  instru- 
ment designed  for  making  a  continuous  record  of  the  pres- 
sure  of  fluids,   either    above  or  below  the  atmosphere,  as 


« 


ordinarily  measured  in  inches  of  water.  It  is  useful  for 
determining  and  recording  the  drafts  of  chimneys,  or  the 
pressure  of  air  in  the  ash  pit  of  a  steam  boiler,  in  mines 
when  forced  therein,  or  in  buildings  when  introduced  for 
heating  and  ventilation  ;  it  will  show  the  pressure  of  gas  for 
illuminating  or  other  purposes  at  the  works  or  at  the  place 
of  consumption,  or  of  any  fluid  where  the  pressure  is  sought 
and  its  record  desired.  This  instrmnent  is  similar  in  the 
character  of  its  work  or  operations  to  the  Crosby  Recording 
Gage,  but  is  adapted  to  conditions  requiring  one  which  is 
more  sensitive  and  delicate. 


THERMOMETERS 


195 


Steam  Pipe 
Thermometer 


Hot  Water 
Thermometer 


Hot  Well  Thermometer 


196 


LANZA    CONTINUOUS   DIAGRAM   APPLIANCE 


THE  LANZA  CONTINUOUS  DIAGRAM   APPLIANCE 
WITH   CROSBY  INDICATORS 

Patented 


The  Lanza  Continuous  Diagram  Appliance  is  not  in  itself 
an  indicator,  but  displaces  the  ordinary  drum  as  a  means 
for  supplying  the  paper  for  taking  indicator  cards,  and  any 
indicator  may  be  combined  or  adapted  for  use  with  it.  It 
is  assembled  upon  a  bracket,  or  frame,  which  is  designed  to 
support  also  the  indicator  and  its  connections  so  that  these 
parts  may  be  rigidly  fixed  in  proper  mutual  relation.  Upon 
this  bracket  are  mounted  the  spindle  for  receiving  the  new 
roll  of  paper,  the  drum  which  feeds  the  paper  forward,  and 
upon  which  the  pencil  point  bears  in  making  the  record,  and 
the  spool  upon  which  the  paper  is  afterward  wound. 

The  drum  is  rotated  continuously  in  one  direction  by 
the  alternate  engagement  of  two  series  of  clutches  controlled 
by  a  cord  passing  over  the  pulley  at  the  extreme  end  of  the 
bracket  arm  and  actuated  by  a  cross-head  block  which  is 


LANZA    CONTINUOUS  DIAGRAM   APPLIANCE  197 

positively  connected  to  the  cross-head  of  the  engine  or  some 
other  convenient  portion  of  the  machinery  which  moves  in 
exact  accordance  with  the  piston.  This  connection  between 
the  cross-head  block  of  the  Continuous  Diagram  Appliance 
and  the  engine  cross-head  is  not  illustrated,  but  it  may  be 
any  reducing  motion  which  will  drive  the  Appliance  positively 
in  both  directions,  on  the  forward  and  backward  strokes,  as 
a  spring  is  not  depended  upon  for  the  return  stroke,  as  in 
ordinary  indicator  drums  and  reducing  motions.  From  this 
peculiar  and  desirable  mode  of  connection  there  must  result 
accuracy  and  positiveness  of  action  in  making  continuous 
records. 

There  are  other  important  details  of  the  Appliance,  such 
as  a  method  of  marking  upon  the  paper  the  end  of  each  stroke 
or  half  revolution  of  the  engine,  mechanically  controlled  by 
contacts  conveniently  arranged  for  easy  adjustment  at  either 
end  of  the  stroke  of  the  cross-head  block,  and  an  atmospheric 
marker  which  is  immediately  adjustable  to  any  required 
position.  Moreover,  Crosby  indicators  afford  further  means 
in  themselves  for  readily  adjusting  the  position  of  the  pencil 
point  to  bring  the  atmospheric  line  at  any  convenient  posi- 
tion upon  the  paper. 

Uses  of  Such  an  Instrument 

Whenever  the  diagrams  corresponding  to  successive 
revolutions  of  an  engine  differ,  the  need  for  a  continuous 
series  of  cards  becomes  apparent,  whether  the  variation  be 
due  to  a  variable  load,  as  in  locomotives,  rolling  mills,  and 
many  stationary  steam  plants,  or  to  the  nature  of  the  opera- 
tions within  the  cylinder,  as  in  gas  engines. 

Thus,  in  the  case  of  a  steam  engine,  single  ordinary  indica- 
tor cards  taken  at  intervals  of  from  three  to  five  minutes  do 
not  exhibit  the  variations  in  consecutive  revolutions  and  do 
not  enable  us  to  determine  the  average  M.  E.  P.  If,  on  the 
other  hand,  a  series  of  diagrams  is  taken  on  the  same  paper, 
as  when  using  the  ordinary  indicator  drum,  the  lines  of  the 
different   cards  become  so   confused,  overlying  each  other, 


198  LANZA    CONTINUOUS   DIAGRAM    APPLIANCE 

that  (a)  it  is  not  possible  to  distinguish  them  sufficiently 
to  obtain  a  record  of  the  variations,  and  (b)  any  attempt  to 
determine  from  them  the  average  M.  E.  P.  results  in  a  con- 
siderable error. 

In  the  case  of  a  gas  engine  a  complete  cycle  of  operations 
involves  a  considerable  number  of  revolutions  of  the  engine, 
and  hence  several  successive  cards  must  be  secured  to  furnish 
complete  information  regarding  what  occurs  and  to  enable  us 
to  determine  the  M.  E.  P.  for  any  given  cycle  of  operations. 
Thus  in  the  case  of  fire  1,  miss  5,  twelve  successive  diagrams 
are  involved,  while  in  the  case  of  fire  8,  miss  4,  twenty-four 
revolutions,  and  hence  twenty-four  successive  diagrams,  are 
involved.  If  the  entire  set  be  taken  on  one  ordinary  indi- 
cator card,  the  lines  (especially  those  in  the  lower  part  of  the 
diagram)  are  so  confused  with  each  other  that  it  is  impossible 
to  separate  them,  and,  if  the  lower  part  of  the  diagram  be 
omitted  or  disregarded,  the  error  may  reach  twenty  per  cent. 


Description  of  the  Diagrams 

On  the  roll  of  paper  will  be  found:  (a)  The  line  traced 
by  the  indicator  pencil.  (6)  The  atmospheric  line,  (c) 
The  continuous  line  drawn  by  the  stroke-marker  pencil,  with 
its  short  vertical  lines  that  mark  the  ends  of  the  stroke. 
The  record  obtained  during  twenty  consecutive  revolutions 
of  a  steam  engine,  for  example,  consists  of  twenty  consec- 
utive cards,  which  are  not  overlapping,  but  clearly  sepa- 
rated. The  nature  of  the  separate  portions  of  the  line  thus 
drawn  by  the  indicator  pencil  and  the  events  of  each  stroke 
are  plainly  seen  on  the  diagram.  The  diagram  obtained 
during  one  complete  cycle  of  operations  of  a  gas  engine,  with 
a  cycle  of  fire  and  miss  strokes,  shows  what  occurs  during  the 
successive  complete  revolutions  of  the  engine,  and  the  nature 
of  the  separate  portions  of  the  line  traced  by  the  indicator 
pencil  indicates  the  events  of  the  strokes.  The  usual  result 
of  taking  such  an  entire  series  on  one  ordinary  indicator 
card  is  a  confusion  of  the  lines  in  the  lower  part  of  the 


LANZA    CONTINUOUS   DIAGRAM   APPLIANCE  199 

diagram,  but  with  this  instrument  all  such  unccrtaintj'  and 
error  is  avoided. 


Determination  of  M.  E.  P.  by  Mearis  of  a  Planimcter  or  an 
Integrator 

Having  taken  a  diagram  corresponding  to  a  certain  num- 
l)er  of  revolutions  of  the  engine  by  means  of  the  Lanza  Con- 
tinuous Diagram  Appliance,  we  must  first  draw  through 
the  points  which  mark  the  ends  of  the  several  strokes  lines 
perpendicular  to  the  atmospheric  line. 

If  we  use  an  ordinary  planimeter,  we  need  only  to  plani- 
meter  the  positive  and  the  negative  areas  separately,  and  then 
to  subtract  the  sum  of  the  negative  areas  from  the  sum  of 
the  positive  areas,  to  oi:)tain  the  total  area  of  the  given  series 
of  cards.  Having  obtained  the  resultant  area  in  this  way, 
we  obtain  the  M.  E.  P.  for  this  diagram  by  first  dividing  it 
by  the  total  length  divided  by  the  number  of  complete  revo- 
lutions, and  then  multiplying  this  average  height  by  the 
scale  of  the  indicator  spring. 

Time  can  be  saved  if  an  integrator  is  used.  It  will  be 
convenient  to  set  the  track  of  the  integrator  approximately 
parallel  to  the  atmospheric  line.  To  obtain  the  area  of  the 
diagrams  corresponding  to  the  successive  revolutions  of  the 
engine,  we  can  start  the  pencil  of  the  integrator  anywhere 
on  the  pressure  line.  In  the  forward  motion  we  must  drag 
the  pencil  of  the  integrator  along  the  line  drawn  by  the  in- 
dicator pencil  for  every  forward  stroke,  and  along  the  at- 
mospheric line  for  every  return  stroke,  while  in  the  return 
motion  we  must  drag  the  pencil  of  the  integrator  along  the 
line  drawn  by  the  pencil  of  the  indicator  for  every  return 
stroke  and  along  the  atmospheric  line  for  every  forward 
stroke.  The  resultant  area  can  then  be  read  off  on  the  in- 
tegrator. Any  line  parallel  to  the  atmosi)heric  could  bo  used 
in  this  operation  instead  of  the  atmospheric,  if  for  any  reason 
jt  were  more  convenient. 


200  LANZA   CONTINUOUS   DIAGRAM   APPLIANCE 

Convenience  in  Taking  Diagrams 

The  paper  can  be  removed  from  the  winding-spindle  when 
the  entire  roll  has  been  used  or  it  can  be  torn  off  at  any  point 
and  the  portion  already  on  the  spool  removed.  The  free 
end  of  the  unused  portion  can  then  be  wound  upon  it  to  com- 
mence the  taking  of  a  new  series  of  diagrams. 

The  mechanism  of  the  instrument  continues  in  operation 
so  long  as  the  connection  to  the  cross-head  or  reducing  motion 
is  in  place,  but  by  means  of  the  pressure  roll,  controlled  by  a 
simple  lever,  the  taking  of  diagrams  can  be  started  or  stopped 
at  any  time  and  continued  at  will. 

Diagrams  can  be  made  by  means  of  this  Appliance  used 
with  Crosby  indicators  as  made  for  steam,  air,  gas,  ammonia 
or  any  liquid,  or  any  ordinary  pressure  indicator  can  be 
adapted  by  simply  disregarding  the  ordinary  drum  and  turn- 
ing the  pencil  linkage  to  bear  upon  the  drum  of  the  instru- 
ment. 

The  Lanza  Continuous  Diagram  Appliance  is  made  only 
by  this  Company.  Full  directions  for  operating  it  are  sent 
with  each  instrument.  A  detailed  description  with  illus- 
trative diagrams  will  be  forwarded  on  application. 


201 


THE   CROSBY   INDICATOR 

It  may  be  of  interest  to  those  Avho  have  read  tliis  book  to 
know  that  whatever  of  merit  in  this  instrument  has  been 
described  and  ilhisti'ated  in  these  pages  has  been  recog- 
nized and  acknowledged  as  follows  : 

At  the  Paris  Exposition  of  1889,  where  it  received  the 
highest  award,  a  gold  medal. 

At  the  AVorld's  Columbian  Exjjosition,  Chicago,  in  1893, 
where  it  received  the  highest  award,  a  medal  and  diploma. 

At  the  Cotton  States  and  International  Exposition  at 
Atlanta,  in  1895,  where  it  received  the  highest  award. 

At  the  Russian  Exposition  held  at  Nijni  Novgorod,  in 
1896,  where  it  received  the  highest  award,  a  gold  medal 
and  diploma  of  honor. 

At  the  Louisiana  Purchase  Exposition,  held  at  St.  Louis 
in  1904,  where  it  received  the  grand  prize. 

The  Crosby  Indicator  is  approved  and  adopted  by  the 
United  States  Govermnent.  It  is  the  standard  in  nearly  all 
the  great  electric  light  and  power  stations  of  the  United 
States.  It  has  been  approved  and  adopted  by  the  principal 
navies,  the  government  shipyards,  and  the  most  eminent 
technical  schools  of  the  world. 

Full  particulars  for  the  proper  care  and  handling  of  the 
Crosby  Indicator  accompany  each  instrument. 

CROSBY  STEAM  GAGE  AND  \\\LVE  COMPANY 

40  Central  Street,  Marshall  Building,  Boston,  Mass. 
44  Dey  Street,  Hudson  Terminal,  New  York,  N.  Y. 
435-437  West  Lake  Street,  Chicago,  111. 
147  Queen  Victoria  Street,  London,  E.  C,  Eng. 


THE  LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

Santa  Barbara 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW. 


A     000  587  488     8 


